To simplify the square root of 20, follow these steps:
1. Factor 20 into its prime factors:
[tex]\[
20 = 2 \times 2 \times 5
\][/tex]
2. Group the factors inside the square root:
[tex]\[
\sqrt{20} = \sqrt{2 \times 2 \times 5}
\][/tex]
3. Identify squares within the factors:
Notice that [tex]\(2 \times 2\)[/tex] is a perfect square, which is [tex]\(4\)[/tex].
4. Take the square root of the perfect square:
[tex]\[
\sqrt{2 \times 2 \times 5} = \sqrt{4 \times 5}
\][/tex]
Since [tex]\(\sqrt{4} = 2\)[/tex], this simplifies further to:
[tex]\[
\sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2 \times \sqrt{5}
\][/tex]
So, the simplified expression for [tex]\(\sqrt{20}\)[/tex] is:
[tex]\[
2\sqrt{5}
\][/tex]
In numerical terms, [tex]\(2\sqrt{5}\)[/tex] evaluates to approximately 4.47213595499958. Therefore, both [tex]\( \sqrt{20} \)[/tex] and [tex]\( 2\sqrt{5} \)[/tex] represent the same value, with the latter being the simplified form.
