Question

Find the cube of positive square root of 25.
$\left( A \right)$ 5
$\left( B \right)$ 25
$\left( C \right)$ 125
$\left( D \right)$ 625

Answer 1

Hint – In this particular type of question use the concept that the square root of any complete square is come as positive, negative times of the number (i.e. square root of 36 which is a complete square is $ \pm 6$) so use this concept to reach the solution of the question.

Complete step-by-step answer:
Given number
25.
Now we have to find out the positive square root of 25.
Let the square root of 25 be A.
So, A = $\sqrt {25} $
Now as we know that the factors of 25 are (5 and 5).
So, A = $\sqrt {5 \times 5} $
Now this is written as
$ \Rightarrow A = \sqrt {{5^2}} $
Now as we know that the value of the square root is always comes as positive and negative so we have,
$ \Rightarrow A = \pm 5$
So this is the square root of 25.
Now as we see it is positive (+5) as well as negative (-5).
And we have to find out the cube of positive square root of 25.
So let the cube of positive square root of 25 be X.
So, X = ${\left( { + 5} \right)^3}$
So this is written as, X = ${\left( { + 1} \right)^3}{\left( 5 \right)^3}$
Now as we know when positive is multiplied together it always remains positive.
So ${\left( { + 1} \right)^3} = 1$
Therefore, X = $1{\left( 5 \right)^3}$
Now as we see above when we multiply 5 two times it comes out to be 25.
So when we multiply 25 by 5 (i.e. 5 three times) it comes out to be 125.
Therefore, $5 \times 5 \times 5 = 125$
Therefore, X = $1{\left( 5 \right)^3}$ = 125.
So the cube of positive square root of 25 is 125.
So this is the required answer.
Hence option (C) is the required answer.

Note – Whenever we face such types of question the key concept we have to remember is that always recall the square root of all complete squares, so first find out the square root of 25 which is stated above, as it is come as $ \pm 5$, and we have to evaluate the positive square root of 25 so we have to consider (+5) so the cube of (+5) is 125, which is the required answer.