To simplify [tex]\(\sqrt{18}\)[/tex], we can break down the process into a few clear steps:
1. Factor the number under the square root:
[tex]\[
18 = 9 \times 2
\][/tex]
2. Express the square root of the product as a product of square roots:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}
\][/tex]
3. Find the square roots of the factors:
- [tex]\(\sqrt{9}\)[/tex] is a perfect square and equals [tex]\(3\)[/tex].
- [tex]\(\sqrt{2}\)[/tex] is an irrational number, approximately equal to [tex]\(1.4142135623730951\)[/tex].
4. Multiply the square roots together:
[tex]\[
\sqrt{18} = 3 \times \sqrt{2}
\][/tex]
Putting it all together, we find that:
[tex]\[
\sqrt{18} = 3 \times 1.4142135623730951 \approx 4.242640687119286
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{18}\)[/tex] is [tex]\(3\sqrt{2}\)[/tex]. And numerically, [tex]\(\sqrt{18}\)[/tex] approximately equals [tex]\(4.242640687119286\)[/tex].
