To simplify [tex]\(\sqrt{18}\)[/tex]:
1. Factorize 18:
- Notice that 18 can be written as a product of its factors: [tex]\(18 = 9 \times 2\)[/tex].
2. Break down the square root:
- Utilize the property of square roots which states that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex].
- Applying this property, we get [tex]\(\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}\)[/tex].
3. Simplify further:
- We know that [tex]\(\sqrt{9} = 3\)[/tex] (since [tex]\(3 \times 3 = 9\)[/tex]).
- Therefore, [tex]\(\sqrt{9} \times \sqrt{2} = 3 \times \sqrt{2}\)[/tex].
4. Conclusion:
- Hence, the simplified form of [tex]\(\sqrt{18}\)[/tex] is [tex]\( 3\sqrt{2} \)[/tex].
Thus, the correct answer is [tex]\( 3\sqrt{2} \)[/tex].
