Simplify 300−−−√ .(1 point)

Question

Responses

This radical expression is already fully simplified.
This radical expression is already fully simplified.

103–√
10 start root 3 end root

512−−√
5 start root 12 end root

1003–√

Answer 1

To simplify \( \sqrt{300} \):

1. First, find the prime factorization of 300: \[ 300 = 3 \times 100 = 3 \times 10^2 = 3 \times (2 \times 5)^2 = 3 \times 2^2 \times 5^2 \]

2. Rewrite \( \sqrt{300} \) using the prime factorization: \[ \sqrt{300} = \sqrt{3 \times 100} = \sqrt{3} \times \sqrt{100} = \sqrt{3} \times 10 \]

3. Thus, the simplified form of \( \sqrt{300} \) is: \[ 10\sqrt{3} \]

So the answer is: 10√3.