select the correct answer. simplify the following radical expression. $sqrt{20}$\na. $2sqrt{5}$\nb…
select the correct answer. simplify the following radical expression. $sqrt{20}$\na. $2sqrt{5}$\nb. $5sqrt{2}$\nc. $4sqrt{5}$\nd. $10sqrt{5}$
Answer
Explanation:
Step1: Factorize the number inside the square - root
We know that (20 = 4\times5), so (\sqrt{20}=\sqrt{4\times5}).
Step2: Use the square - root property (\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}) ((a = 4), (b = 5))
(\sqrt{4\times5}=\sqrt{4}\cdot\sqrt{5}).
Step3: Calculate (\sqrt{4})
Since (\sqrt{4}=2), then (\sqrt{4}\cdot\sqrt{5}=2\sqrt{5}).
Answer:
A. (2\sqrt{5})