Question

Simplify ^3√135

3^3√5

5^3√5

27^3√5

25^3√3

Answer 1

∛135 = 3∛5

Step-by-step explanation:

∛135 = ∛(27×5) = ∛27 × ∛5 = 3∛5

As with any root, the root of a product is the product of the roots of the factors. Here, the only cubic factor is 27 = 3³.

_____

Comment on powers and roots

It can help immensely if you are familiar with the squares and cubes of small integers. Of course, your knowledge of regular times tables will get you to the fact that ...

... 27 = 3·9 = 3·3·3 = 3³

Knowledge of divisibility rules is helpful, too. Here, you can see that 135 ends in 5, so you know that 5 is a factor of the number.

Answer 2

∛135 = 3∛5

Step-by-step explanation:

∛135 = ∛(27×5) = ∛27 × ∛5 = 3∛5

As with any root, the root of a product is the product of the roots of the factors. Here, the only cubic factor is 27 = 3³.

_____

Comment on powers and roots

It can help immensely if you are familiar with the squares and cubes of small integers. Of course, your knowledge of regular times tables will get you to the fact that ...

... 27 = 3·9 = 3·3·3 = 3³

Knowledge of divisibility rules is helpful, too. Here, you can see that 135 ends in 5, so you know that 5 is a factor of the number.