Question

Write $\sqrt[3]{{80}}$ in radical form.

Answer 1

Hint: We have been given a number $\sqrt[3]{{80}}$ and we need to write it in radical form i.e., we simply need to find its cube root.
For that, we need to find all the prime factors $80$ and make triplets and then take them out of the root as one.

Complete step-by-step answer:
Given number is $80$ and we need to write it in radical form.
First, we’ll find its prime factors, which are, $2,2,2,2,5$ ,
i.e., $80$ can be written as $2 \times 2 \times 2 \times 2 \times 5$ .
Now, only $2$ makes a triplet, i.e., $\underline {2 \times 2 \times 2} \times 2 \times 5$ and one $2$ and $5$ are left out.
So, we’ll take this triplet out of the root as one and we’ll get $2\sqrt[3]{{2 \times 5}}$ i.e., $\sqrt[3]{{80}}$ can be written as $2\sqrt[3]{{2 \times 5}}$ .
Now, since, $2$ and $5$ does not make any triplet, so they will remain as it is, inside the cube root.
Hence, the radical form of $\sqrt[3]{{80}}$ is $2\sqrt[3]{{10}}$ .

Note: Radical form is nothing but simply the simplest form of the number.
In this question, we have directly used the prime factorization of $80$ as $80 = 2 \times 2 \times 2 \times 2 \times 5$ .
So, for that, we need to check the prime numbers, which are factors of $80$ .
Now, since we need to find the cube root of $80$ , that is why we take the factors outside the root in triplets.
Similarly, if we need to take a square root, then we’ll take factors outside the roots in pairs, parallelly, if we have to take the fourth root of a number, then we have to take factors in a group of four, outside the square root and so on.
The factors which do not make a triplet will be left inside the root and we will simply multiply them.