To simplify the radical expression [tex]\(\sqrt{20}\)[/tex], we need to look for perfect square factors of 20. Here’s the detailed step-by-step process:
1. Identify factors of 20:
The number 20 can be factored into [tex]\( 4 \times 5 \)[/tex].
2. Simplify the square root:
Since 4 is a perfect square ([tex]\(4 = 2^2\)[/tex]), we can split the expression using the properties of square roots:
[tex]\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5}
\][/tex]
3. Calculate the square root of the perfect square:
We know that [tex]\(\sqrt{4} = 2\)[/tex], so substituting this in:
[tex]\[
\sqrt{4} \times \sqrt{5} = 2 \times \sqrt{5}
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{20}\)[/tex] is:
[tex]\[
2 \sqrt{5}
\][/tex]
Thus, the correct answer is [tex]\( \boxed{2 \sqrt{5}} \)[/tex].
