To simplify [tex]\(\sqrt{8}\)[/tex], let's break it down step by step.
1. Factor the number under the square root:
Start by expressing 8 as the product of its prime factors:
[tex]\[
8 = 4 \times 2
\][/tex]
2. Rewrite the square root using the factors:
[tex]\[
\sqrt{8} = \sqrt{4 \times 2}
\][/tex]
3. Apply the property of square roots to separate the factors:
Recall that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]. Using this property:
[tex]\[
\sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2}
\][/tex]
4. Simplify the square roots:
We know that [tex]\(\sqrt{4} = 2\)[/tex], so we can simplify further:
[tex]\[
\sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2}
\][/tex]
Thus, the simplified form of [tex]\(\sqrt{8}\)[/tex] is:
[tex]\[
2 \times \sqrt{2}
\][/tex]
To express this in numeric terms:
[tex]\[
2 \times \sqrt{2} \approx 2 \times 1.414213562 \approx 2.8284271247461903
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{8}\)[/tex] is [tex]\(2 \times \sqrt{2}\)[/tex] and its numeric approximation is approximately [tex]\(2.8284271247461903\)[/tex].
