Products of Irrational Square Roots Quick Check

Question

2 of 52 of 5 Items
Question
What is the irrational square root √28
simplified?(1 point)
Responses

√4 ⋅ √7
start root 4 end root times start root 7 end root

√214
2 start root 14 end root

√27
2 start root 7 end root

√47
4 start root 7 end root
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Answer 1

To simplify the irrational square root \(\sqrt{28}\), we need to factor it into a product of square roots of perfect squares.

1. First, we can factor \(28\) as \(4 \times 7\), where \(4\) is a perfect square.
2. Therefore, we can rewrite \(\sqrt{28}\) as follows: \[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7} \]

So, the simplified form of \(\sqrt{28}\) is \(2\sqrt{7}\).

The correct response from the given options is:

• \(2 \sqrt{7}\).