Question

the sum of a no and its positive square roots is 6/25.find the number

Answer 1

let no be x
then
x +x^2 =6/25
x^2=6×/25
×^2/×=6×/25×
×=6/25
so no. is 6/25.

Answer 2

Answer: The number is $\dfrac{1}{25}.$

Step-by-step explanation:  Let the required number be represented by 'p'.

Then, according to the given information, we have

$p+\sqrt p=\dfrac{6}{25}.~~~~~~~~~~~~~~(i)$

Let us consider that x² = p, where 'x' is the positive square root of 'p'.

Therefore, equation (i) can be written as

$x^2+x=\dfrac{6}{25}\\\\\Rightarrow 25x^2+25x=6\\\\\Rightarrow 25x^2+25x-6=0\\\\\Rightarrow 25x^2+30x-5x-6=0\\\\\Rightarrow 5x(5x+6)-1(5x+6)=0\\\\\Rightarrow (5x-1)(5x+6)=0\\\\\Rightarrow 5x-1=0,~~~~~~5x+6=0\\\\\Rightarrow x=\dfrac{1}{5},~~~~~~~~\Rightarrow x=-\dfrac{6}{5}.$

Since 'x' is the positive square root of 'p', so it cannot be negative.

Therefore, we must have

$x=\dfrac{1}{5}\\\\\Rightarrow x^2=\dfrac{1}{25}\\\\\Rightarrow p=\dfrac{1}{25}.$

Thus, the required number is $\dfrac{1}{25}.$