Question

Find the cube root of \[{\mathbf{72}}\] ?

Answer 1

Hint: In this problem, we have to find the cube root of \[72\] . First of all we will write \[72\] as the products of prime factors.
We will use Euclid division lemma for finding the primes. Then we will find the cubic root by selecting three prime factors for one and leaving others that are not in pairs of three.

Complete step-by-step answer:
First of all we use the Euclid division lemma to find the prime factors and then we write the given number as a product of prime numbers.
This \[72\] can be written as \[72 = 2 \times 2 \times 2 \times 3 \times 3\].
Now we find the cubic root as follow:
\[\sqrt[3]{{72}} = \sqrt[3]{{2 \times 2 \times 2 \times 3 \times 3}}\]
Now we move \[2\] out of the cubic root as it is in pairs of three tuples.
Hence cube root of \[72\] in its lowest radical form be written as
\[\sqrt[3]{{72}} = 2 \times \sqrt[3]{{3 \times 3}}\]
i.e. \[\sqrt[3]{{72}} = 2\sqrt[3]{9}\]
Hence, the cube root of \[72\]is \[2\sqrt[3]{9}\].
So, the correct answer is “ \[2\sqrt[3]{9}\]”.

Note: Cube of any number is the product of the same number multiplied by itself thrice times.
For example: \[{5^3} = 5 \times 5 \times 5 = 125\]
Cubic root or cube root of a number is another number which when multiplied by itself thrice gives the same number of which it is the cube root it is of. It is denoted by \[\sqrt[3]{{}}\].
For example: The cubic root of 125 is 5. i.e. When \[5\] is multiplied by itself thrice we get\[125\] .