Question

Find the cube root of \[216\] factorization .

Answer 1

Hint : In this question , first we have to know what cube root is . A cube root is a number that can be multiplied by itself three times to equal the original value. Finding a cube root is the opposite of cubing a number or raising a number to the third power. For ex : cube root of $y$ will be $x$ if $y = x \times x \times x$.

Complete step-by-step answer: -
Here we have to find cube root of \[216\]
So in our case we need to figure out what number will multiply by itself three times to give us \[216\]. In other words ,we need to solve for $x$ in the equation seen here
$ \Rightarrow {x^2} = 216$ ………(i)
According to the question, we have to find the cube root by factorisation. So let’s start doing factors of \[216\].
$
   \Rightarrow 216 = 2 \times (108) \\
   \Rightarrow 216 = 2 \times 2 \times (54) \\
   \Rightarrow 216 = 2 \times 2 \times 2 \times (27) \\
   \Rightarrow 216 = 2 \times 2 \times 2 \times 3 \times (9) \\
   \Rightarrow 216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \\
$
We cannot factorise this more , hence
We can also write this as :
$
   \Rightarrow 216 = (2 \times 3) \times (2 \times 3) \times (2 \times 3) \\
   \Rightarrow 216 = 6 \times 6 \times 6 \\
$
Here we can clearly see that , when we multiply 6 by itself three times ,we will get \[216\]
Therefore , cube root of \[216\], $\sqrt[3]{{216}} = 6$.

Note : In this type of question, we will simply use the method of factorization . we have given a number and we have to make factors of that number in such a way that when we multiply one of its common factors by itself three times ,we will get the required number . then we can say that the cube root of the given number is that common factor.