The sum of a number and its positive square root is $\frac{6}{25}$. Find the number.

Given:

The sum of a number and its positive square root is $\frac{6}{25}$.

 To do:

We have to find the number.

Solution:

Let the required number be $x^2$.

This implies,

The positive square root of the number is $x$.

According to the question,

$x^2+x=\frac{6}{25}$

$25(x^2+x)=6$

$25x^2+25x-6=0$

Solving for $x$ by factorization method, we get,

$25x^2+30x-5x-6=0$

$5x(5x-1)+6(5x-1)=0$

$(5x+6)(5x-1)=0$

$5x+6=0$ or $5x-1=0$

$5x=-6$ or $5x=1$

$x=\frac{-6}{5}$ or $x=\frac{1}{5}$

The square root of the required number is positive. Therefore, $x=\frac{1}{5}$

$x^2=(\frac{1}{5})^2=\frac{1}{25}$

The required number is $\frac{1}{25}$.

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Updated on: 10-Oct-2022

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