Question

Which is like a radical to ^3 to the square root of 54 after simplifying

Answer 1

The radical that is equal to ∛54 is 3∛2.

Explanation:

Given

∛54

We need to find the radical that is similar to ∛54, we need to break down the radicand 54, into smaller numbers, therefore, take the LCM of the number,

54 = 2 x 3 x 3 x 3

As we are taking the cube root, therefore, we need numbers that are repeating thrice.

Thus, the radical can be written as,

`\sqrt[3]{54} =\sqrt[3]{2x 3x 3x 3} \\\\\sqrt[3]{54} =3\sqrt[3]{2}`

Hence, the radical that is equal to ∛54 is 3∛2

Answer 2

`3\sqrt[3]{2}`

Explanation:

Original expression:

`\implies \sqrt[3]{54}`

Factorize 54 using prime factorization:

`\implies \sqrt[3]{2 \cdot 3^3}`

Apply radical rule:
`\sqrt[n]{ab} =\sqrt[n]{a} \cdot \sqrt[n]{b}`

`\implies \sqrt[3]{2} \cdot \sqrt[3]{3^3}`

Apply radical rule:
`\sqrt[n]{a^n} =a`

`\implies \sqrt[3]{2} \cdot 3`

`\implies 3\sqrt[3]{2}`