Question

: For question 1, answer in complete sentences using math vocabulary. 1. How does simplifying a square root expression differ from simplifying a cube root expression?

Answer 1

Explanation:

You want to know how simplifying a square root expression differs from simplifying a cube root expression.

Simplifying radicals

A radical is simplified by removing factors that have exponents that are a multiple of the index of the radical. The difference between a square root and a cube root is that the index is different.

The index of a square root is 2, so perfect square factors can be removed from under the radical.

The index of a cube root is 3, so perfect cube factors can be removed from under the radical.

Here are some examples.

`√(80)=√(4^2\cdot5)=4√(5)\\\\\sqrt[3]{80}=\sqrt[3]{2^3\cdot10}=2\sqrt[3]{10}`

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