Numbers

Number Theory Level 1

There is a number between $30$ and $40$ which is a square number and also a triangle number. What is the number?

7 solutions

Joseph Gomes
Feb 20, 2014

$36={6}^{2}=\frac{8\,\left( 8+1\right) }{2}$

Are we all Asian?

Raj Thaker - 7 years, 3 months ago

Perfect solution !!

Prasun Biswas - 7 years, 3 months ago

Mohammad Khaza
Aug 1, 2017

$5^2=25$

$6^2=36$ ...............[the answer]

$7^2=49$

so,the only square number between 30 and 40 is 36

Arpit Sah
Feb 17, 2014

There is only one square number between 30 and 40 which is 36 .

Rocky Roy - 7 years, 3 months ago

thats what, u r correct arpit.

pulkit gopalani - 7 years, 3 months ago

You should also show that how $36$ is a triangular number !!

Prasun Biswas - 7 years, 3 months ago

I didn't really understand the meaning of Triangle number

Mahmoud El-Kady - 7 years, 3 months ago

A triangular number is such a number which can be represented in the form $\frac{n(n+1)}{2}$ where $n$ be a natural number.

Like, $36$ here can be represented in the form $\frac{8(8+1)}{2}$ i.e., in the form $\frac{n(n+1)}{2}$ with $n=8$

Prasun Biswas - 7 years, 3 months ago

Mahmoud, see https://en.wikipedia.org/wiki/Triangle_number.

Bill Bell - 6 years, 10 months ago

yeah that's true :)

Christine Gutierrez - 7 years, 1 month ago

HAHA I thought that first

Kent Adoniram Paguinto - 6 years, 10 months ago

Syed Hamza Khalid
Oct 19, 2017

The only square number between $30$ and $40$ is

$\large \color{#3D99F6}36$

Hassam Rind
Apr 8, 2014

the number between 30 and 40 is 36 which is square of 6 and also a triangle number

Sathyanarayana Rao
Mar 4, 2014

1+2+3+4+5+6+7+8 =36

Zoha Abid
Feb 28, 2014

36 is a square no.