Question

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

• A. $5$
• B. $\frac{1}{5}$
• C. $25$
• D. $\frac{1}{25}$

Answer 1

The correct option is D $\frac{1}{25}$

Let the number be $x$.
$x+\sqrt{x}=\frac{6}{25}$ $\Rightarrow \sqrt{x}=\frac{6}{25}-x$
Now, squaring on the both sides, we get
$x=\frac{36}{625}+x^2-\frac{12x}{25}$

$\therefore x^2-\frac{37x}{25}+\frac{36}{625}=0$

$\therefore x=\frac{36}{25},\frac{1}{25}$