Question

For what positive number is the square root of the number the same as the number divided by $40$?

• A. 1400
• B. 1500
• C. 1600
• D. 1700

Answer 1

Answer: (C)

1600

Let the number be ${}^{\prime }{n}^{\prime }$

Given that, square root of the number is same as the number when divided by ${}^{\prime }{40}^{\prime }$

Formally, we can write it as

$\sqrt{n}$ $=$ $\frac{n}{40}$

Squaring on both sides, we get

$n$ $=$ $\frac{n^2}{{40}^2}$

Rearranging the terms, we get

$\frac{n^2}{n}$ $=$${40}^2$

$\Rightarrow n$ $=$ $40$ $\times$ $40$ ........ $(n$ $>$ $0)$

$\Rightarrow n$ $=$ $1600$

Therefore, the number is ${}^{\prime }{1600}^{\prime }$.