Add and Subtract Radicals Quick Check

Question

1 of 51 of 5 Items
Question
Add 321−−√ + 721−−√
.(1 point)
Responses

24 −−−√ + 28−−√
Start Root 24 End Root plus Start Root 28 End Root

1042−−√
10 Start Root 42 End Root

1021−−√
10 Start Root 21 End Root

52−−√

Answer 1

To simplify the expression \( \sqrt{32} + \sqrt{72} \), we can start by simplifying each square root.

1. Simplifying \( \sqrt{32} \): \[ \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \]

2. Simplifying \( \sqrt{72} \): \[ \sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2} \]

Now we can add the two simplified forms together: \[ \sqrt{32} + \sqrt{72} = 4\sqrt{2} + 6\sqrt{2} = (4 + 6)\sqrt{2} = 10\sqrt{2} \]

Therefore, the correct response is: \[ 10\sqrt{2} \]

So the correct answer to the question is: 10√21.