Question

A positive number exceeds its square root
by 30. Find the number

Answer 1

Answer:

36

Step-by-step explanation:

Given : A positive number exceeds its square root  by 30.

To Find :  Find the number

Solution:

Let the number be x

Since we are given that  A positive number exceeds its square root  by 30.

So, $x-\sqrt{x}=30$

$x-\sqrt{x}=30$

$(\sqrt{x}-1)\sqrt{x}=30$

$\sqrt{x}=6$

$x=36$

Hence the number is 36

Answer 2

Answer:

$Required\: number =36\:Or\:25$

Step-by-step explanation:

Let the positive number = x

$Square \:root \:of \: the \:number = \sqrt{x}$

According to the problem given,

$x-\sqrt{x}=30$

$\implies x-30=\sqrt{x}$

$\implies (x-30)^{2}=(\sqrt{x})^{2}$

$\implies x^{2}-2\times x\times 30+(30)^{2}=x$

$\implies x^{2}-60x-x+900=0$

$\implies x^{2}-61x+900=0$

$\implies x^{2}-36x-25x+900=0$

$\implies x(x-36)-25(x-36)=0$

$\implies (x-36)(x-25)=0$

$\implies x-36=0\:Or\:x-25=0$

$\implies x=36\:Or\:x=25$

Therefore,

$Required\: number =36\:Or\:25$

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