Question

Cube root of a number when divided by $ 5 $ results in $ 25 $ , what is the number?
(A) $ 5 $
(B) $ {125^3} $
(C) $ {5^2} $
(D) $ 125 $

Answer 1

Hint: This question is based on the number system. In order to solve this question, we need to know about the cube and the cube roots of a number. A cube of the number is obtained when we multiply the number three times to itself and cube root of the number denoted by this symbol $ \sqrt[3]{{}} $ is obtained when we raise the power of the number to $ \dfrac{1}{3} $ .
For example, the cube of the number $ 2 $ is,
 $ \begin{array}{c}
{2^3} = 2 \times 2 \times 2\\
 = 8
\end{array} $
And the cube root of the number $ 8 $ is,
 $ \begin{array}{c}
\sqrt[3]{8} = {8^{\dfrac{1}{3}}}\\
 = 2
\end{array} $

Complete step-by-step answer:
Let us assume the number is $ n $ .
Now according to the question, when the cube root of this number $ n $ is divided by $ 5 $ then, it results in $ 25 $ .

 $ \begin{array}{c}
\dfrac{{{\text{Cube root of the number n}}}}{5} = 25\\
\dfrac{{\sqrt[3]{n}}}{5} = 25
\end{array} $
Solving this step by step, we get,
$ \begin{array}{c}
\sqrt[3]{n} = 25 \times 5\\
\sqrt[3]{n} = 125
\end{array} $
We know that in order to remove the cube root of a number, we have to raise the power of that number to $ 3 $ .
So, now remove the cube root by taking the cube of both sides we get,
 $ n = {125^3} $
Therefore, the value of the number $ n $ is $ {125^3} $ and the correct option is (B) $ {125^3} $
So, the correct answer is “Option B”.

Note: It should be noted that we do not need to multiply and solve for $ {125^3} $ as we have achieved our answer, but if solved further, the answer would be given by-
 $ \begin{array}{c}
{125^3} = 125 \times 125 \times 125\\
= 1953125
\end{array} $
And by the definition of the cube root of a number, the value of the cube root of this number would be-
$ {\left( {1953125} \right)^{\dfrac{1}{3}}} = 125 $