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Square Number

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Huỳnh Anh Phương
22/06/2018 at 02:18
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If a is a greatest 1-digit square number, b is  the greatest the even 1-digit number, what is the answer of b+a:0,5?

Square Number

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    Nguyễn Mạnh Hùng 22/06/2018 at 02:23

    According to the title, we have: a = 9

    b = 8

    So b + a : 0,5 = 8 + 9 : 0,5 = 8 + 18 = 26 :) 

    Huỳnh Anh Phương selected this answer.

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huynh anh phuong
22/05/2018 at 11:17
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2
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We have x2=6400.Prove that x it isn't square number.

Square Number

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    Dao Trong Luan Coordinator 22/05/2018 at 11:36

    x2 = 6400 

    \(\Rightarrow x=\pm\sqrt{6400}\)

    \(\Rightarrow x=\pm80\)

    * x = 80 => x isn't a square number

    * x = -80 < 0 isn't  square number

    So................

    huynh anh phuong selected this answer.
  • ...
    Huy Toàn 8A (TL) 23/05/2018 at 01:05

    We have : x2 = 6400

    => x2 = \(\pm80^2\)

    To try on:

    - x = 80 => x it isn't a square number

    - x = -80 < 0 it isn't square number

    => x it isn't square number


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Đỗ Phi Phi
26/07/2017 at 21:31
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2
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a rectangle rug is 3 times as long as it is wide. If it were 3m shorter and 3m wider it would be a square. How long, in metres, is the rug?

wideSquare Numbermetres

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    FA KAKALOTS 19/02/2018 at 20:50

    We have this equation{a=3ba−3=b+3

    (with a is the length and b is the width)

    ⇒3b−3=b+3

    ⇒3b=b+6

    ⇒2b=6

    ⇒b=3

    ⇒a=9

    So that the rug is 3m wide and 9m long.

  • ...
    Son Nguyen Cong 30/07/2017 at 15:42

    We have this equation\(\left\{{}\begin{matrix}a=3b\\a-3=b+3\end{matrix}\right.\)(with a is the length and b is the width)

    \(\Rightarrow3b-3=b+3\)

    \(\Rightarrow3b=b+6\)

    \(\Rightarrow2b=6\)

    \(\Rightarrow b=3\)

    \(\Rightarrow a=9\)

    So that the rug is 3m wide and 9m long.


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taylor swift
27/03/2017 at 11:29
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5
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Find a value of n that satisfies the following:

(a) \(\dfrac{n}{3}\)is a square number

(b) \(\dfrac{n}{5}\)is a cubic number, A cubic number has the form a x a x a = a3

Square Number

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:49

    (a) Assume that the square number 16 = 42 is equal to\(\dfrac{n}{3}\),so n = 48

    (b) Assume that the cubic number 27 = 33 is equal to\(\dfrac{n}{5}\),so n = 135

    Selected by MathYouLike
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    FA KAKALOTS 19/02/2018 at 20:50

    (a) Assume that the square number 16 = 42 is equal ton3n3,so n = 48

    (b) Assume that the cubic number 27 = 33 is equal ton5n5,so n = 135

     1 Selected by MathYou

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    Indratreinpro 05/04/2017 at 13:11

    (a) Assume that the square number 16 = 42 is equal ton3n3,so n = 48

    (b) Assume that the cubic number 27 = 33 is equal ton5n5,so n = 135

     1 Selected by MathYou


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selena gomez
27/03/2017 at 11:26
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4
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A number n becomes a square number when 6 is subtracted from it. The sum of n and 19 is another square number, Find the value of n

Square Number

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:52

    The difference between 2 square numbers in the question is : 
    (n + 19) - (n - 6) = 25

    So those square numbers must be 0 and 25.Then that number is 6

    Selected by MathYouLike
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    FA KAKALOTS 19/02/2018 at 20:50

    The difference between 2 square numbers in the question is : 
    (n + 19) - (n - 6) = 25

    So those square numbers must be 0 and 25.Then that number is 6

    Selected by MathYou

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    Nếu bây giờ ngỏ ý . Liệu có còn kịp không 28/03/2017 at 12:30

    The difference between 2 square numbers in the question is : 
    (n + 19) - (n - 6) = 25

    So those square numbers must be 0 and 25.Then that number is 6

     

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selena gomez
27/03/2017 at 11:25
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0
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Find the greatest value of prime number P in 1991P + 1, so the sum is a square number

Square Number


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selena gomez
27/03/2017 at 11:24
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2
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Given that 24a + 96b is a square number, where a and b are positive integers. Find the latest value of a + b

Square Number

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    FA KAKALOTS 19/02/2018 at 20:51

    24a + 96b = 4(6a + 24b) 

    4 is a square number,so 24a + 96b is a square number only when

    6a + 24b is a square number

    a,b are positive integers⇒a,b ≥ 1⇒ 6a + 24b ≥ 30

    When a + b gets the least value,so does 6a + 24b.Hence,6a + 24b = 36

    ⇒24b < 36 ⇒24b = 24⇒{6a=12b=1⇒{a=2b=1

    => a + b = 3

    So 3 is the least value of a + b

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    Phan Thanh Tinh Coordinator 24/04/2017 at 16:46

    24a + 96b = 4(6a + 24b) 

    4 is a square number,so 24a + 96b is a square number only when

    6a + 24b is a square number

    a,b are positive integers⇒a,b ≥ 1⇒ 6a + 24b ≥ 30

    When a + b gets the least value,so does 6a + 24b.Hence,6a + 24b = 36

    ⇒24b < 36 ⇒24b = 24\(\Rightarrow\left\{{}\begin{matrix}6a=12\\b=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=2\\b=1\end{matrix}\right.\)=> a + b = 3

    So 3 is the least value of a + b


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selena gomez
27/03/2017 at 11:22
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Given a = 123456789 and x is the ones digit of a2 . y and z the tens and hundreds digits of a2 respectively . Find the value of x + y + z.

Square Number


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selena gomez
27/03/2017 at 11:20
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4
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(100 + n) is a square number. (151 + n) is another square number. Find the value of n.

Square Number

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:56

    The difference between 2 above square numbers is :

    (151 + n) - (100 + n) = 51

    So those square numbers must be 49 and 100.Then n = -51

    Selected by MathYouLike
  • ...
    FA KAKALOTS 19/02/2018 at 20:51

    The difference between 2 above square numbers is :

    (151 + n) - (100 + n) = 51

    So those square numbers must be 49 and 100.Then n = -51

  • ...
    »ﻲ2004#ﻲ« 29/03/2017 at 06:11

    The difference between 2 above square numbers is :

    (151 + n) - (100 + n) = 51

    So those square numbers must be 49 and 100.Then n = -51

     

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selena gomez
27/03/2017 at 11:16
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2
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It is given

1 x 2 x 3 x 4 + 1 = 25 = 52

2 x 3 x 4 x 5 + 1 = 121 = 112

3 x 4 x 5 x 6 + 1 = 361 = 192

4 x 5 x 6 x 7 +  1 = 841 = 292

5 x 6 x 7 x 8 + 1 = 1681 = 412

Find 2006 x 2007 x 2008 x 2009 + 1

Square Number

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    FA KAKALOTS 19/02/2018 at 20:51

    We have :

    n(n + 1)(n + 2)(n + 3) + 1 = [n(n + 3)][(n + 1)(n + 2)] + 1

    = (n2 + 3n)(n2 + 3n + 2) + 1 = (n2 + 3n)2 + 2.(n2 + 3n) + 12 

    = (n2 + 3n + 1)2

    Replace n = 2006 into the expression,we have :

    2006 x 2007 x 2008 x 2009 + 1

    = (20062 + 3 x 2006 + 1)2 = 40300552

  • ...
    Phan Thanh Tinh Coordinator 23/04/2017 at 08:24

    We have :

    n(n + 1)(n + 2)(n + 3) + 1 = [n(n + 3)][(n + 1)(n + 2)] + 1

    = (n2 + 3n)(n2 + 3n + 2) + 1 = (n2 + 3n)2 + 2.(n2 + 3n) + 12 

    = (n2 + 3n + 1)2

    Replace n = 2006 into the expression,we have :

    2006 x 2007 x 2008 x 2009 + 1

    = (20062 + 3 x 2006 + 1)2 = 40300552


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selena gomez
27/03/2017 at 11:14
Answers
2
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Devise a formula for the computation of the nth term for

152 = 225

252 = 625

352 = 1225

452 = 2025

Square Number

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    FA KAKALOTS 19/02/2018 at 20:51

    The nth term is

    ¯¯¯¯¯¯¯¯¯¯¯(n)52=(10n+5)2=100n2+100n+25=100n(n+1)+25

    =¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯[n(n+1)]25

    Example :

    To find the 20th term,we calculate 20(20 + 1) = 420

    So the answer is 42025

  • ...
    Phan Thanh Tinh Coordinator 20/04/2017 at 22:08

    The nth term is

    \(\overline{\left(n\right)5}^2=\left(10n+5\right)^2=100n^2+100n+25=100n\left(n+1\right)+25\)

    \(=\overline{\left[n\left(n+1\right)\right]25}\)

    Example :

    To find the 20th term,we calculate 20(20 + 1) = 420

    So the answer is 42025


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selena gomez
27/03/2017 at 11:11
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Find a positive value of m such that 36 + 37 + 38 + 3m + 310 is a square number

Square Number


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selena gomez
27/03/2017 at 11:08
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2
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The number of student in Balmoral High School in 2008 is a square number. The number of students increased by 184 in 2009 and is still a square number. The school had x students in 2008.

Find x ?

Square Number

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    FA KAKALOTS 19/02/2018 at 20:52

    The difference between 2 above square number is 184,so those number are 441 and 625.

    Then x = 441

  • ...
    Phan Thanh Tinh Coordinator 30/03/2017 at 06:44

    The difference between 2 above square number is 184,so those number are 441 and 625.

    Then x = 441


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steve jobs
27/03/2017 at 10:59
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5
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It is given a + b = 14 and ab - ba = n2 The value of n is

Square Number

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    FA KAKALOTS 19/02/2018 at 20:52

    You should check the question.This problem is easy

    ab - ba = 0,so n2 = 0.Then n = 0

  • ...
    »ﻲ2004#ﻲ« 29/03/2017 at 06:10

    You should check the question.This problem is easy

    ab - ba = 0,so n2 = 0.Then n = 0

     
  • ...
    Nguyen Trong Quang 03/09/2019 at 10:08

    Do you think its  ab - ba = n^2?


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steve jobs
27/03/2017 at 10:58
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Find the value of P so that 2P3 + P2 + 18 is a square number

Square Number


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steve jobs
27/03/2017 at 10:57
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0
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The square of the number 123456789 is an n-digit number. The value of n is

Square Number


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Donald Trump
20/03/2017 at 13:47
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1
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Find the \(1001^{st}\) term in

\(2^2-1^2=3\)

\(3^2-2^2=5\)

\(4^2-3^2=7\)

\(3^2-1^2=8\)

\(5^2-4^2=9\)

\(⋮\)

Square Number

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    In the name of love 20/03/2017 at 14:42

    501^2-500^2


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Donald Trump
20/03/2017 at 13:44
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1
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Geven that a is an odd number, show that \(\left(a^2-1\right)\) is a multiple of 8.

Square Number

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    In the name of love 20/03/2017 at 15:19

    a =3;a= -3

    Ya :3 


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Donald Trump
20/03/2017 at 13:42
Answers
3
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The oattern for the sum of consecutive even numbers befinning from 2 is as follows:

 \(2=2=1\times2\)

\(2+4=6=2\times3\)

\(2+4+6=12=3\times4\)

\(2+4+6+8=20=4\times5\)

\(2+4+6+8+10=30=5\times6\)

\(⋮\)

Devise an expression for the sum of n consecutive even numbers.

Square Number

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    FA KAKALOTS 19/02/2018 at 20:52

    Given a sum :  2 + 4 + 6 + ... + 2k

    The number of terms is : 2k−22+1=k

     ( terms )

    So, the result of this sum is : k.(2k+2)2=k.(k+1)

    Example : 2 + 4 + 6 = 2 + 4 + 2.3 ; so k = 3; then 2 + 4 +6 = k.(k+1)=3.4 .

  • ...
    Indratreinpro 05/04/2017 at 13:13

    Given a sum :  2 + 4 + 6 + ... + 2k

    The number of terms is : 2k−22+1=k2k−22+1=k ( terms )

    So, the result of this sum is : k.(2k+2)2=k.(k+1)k.(2k+2)2=k.(k+1)

    Example : 2 + 4 + 6 = 2 + 4 + 2.3 ; so k = 3; then 2 + 4 +6 = k.(k+1)=3.4 .

  • ...
    Run my EDM 21/03/2017 at 21:17

    Given a sum :  2 + 4 + 6 + ... + 2k

    The number of terms is : \(\dfrac{2k-2}{2}+1=k\) ( terms )

    So, the result of this sum is : \(\dfrac{k.\left(2k+2\right)}{2}=k.\left(k+1\right)\)

    Example : 2 + 4 + 6 = 2 + 4 + 2.3 ; so k = 3; then 2 + 4 +6 = k.(k+1)=3.4 .


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Donald Trump
20/03/2017 at 11:22
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8
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It is given \(\dfrac{ab}{a+b}=8\). The value of (a+b) is a square number. Find a and b.

Square Number

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    »ﻲ†hïếu๖ۣۜGïลﻲ« 25/03/2017 at 19:06

    We have : ab = 8(a + b) 

    => 10a + b = 8a + 8b

    => 10a - 8a = 8b - b

    => 2a = 7b

    => a = 7 ; b = 2

    So ab is 72

  • ...
    Trịnh Đức Phát 22/03/2017 at 20:43

    We have : ab = 8(a + b) 

    => 10a + b = 8a + 8b

    => 10a - 8a = 8b - b

    => 2a = 7b

    => a = 7 ; b = 2

    So ab is 72

  • ...
    →இے๖ۣۜQuỳnh 22/03/2017 at 20:20

    We have : ab = 8(a + b) 

    => 10a + b = 8a + 8b

    => 10a - 8a = 8b - b

    => 2a = 7b

    => a = 7 ; b = 2

    So ab is 72

     
     

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