Multiply and Divide Radicals Quick Check

Question

3 of 53 of 5 Items
Question
Divide 4√10/√2
. Provide an exact answer. (1 point)
Responses

4√5
4 start root 5 end root

This expression is already simplified and cannot be divided further.
This expression is already simplified and cannot be divided further.

2√5
2 start root 5 end root

2√10
2 start root 10 end root
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Answer 1

To divide \( \frac{4\sqrt{10}}{\sqrt{2}} \), you can simplify it as follows:

1. Use the property of radicals that states \( \sqrt{a}/\sqrt{b} = \sqrt{a/b} \): \[ \frac{4\sqrt{10}}{\sqrt{2}} = 4 \cdot \frac{\sqrt{10}}{\sqrt{2}} = 4\sqrt{\frac{10}{2}} = 4\sqrt{5} \]

So the exact answer is:

4√5