To simplify the expression [tex]\(2 \sqrt{54}\)[/tex], follow these steps:
1. Factorize the number inside the square root:
Notice that [tex]\(54\)[/tex] can be factored as [tex]\(54 = 9 \times 6\)[/tex].
2. Use the property of square roots:
The square root of a product is the product of the square roots:
[tex]\[
\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6}
\][/tex]
3. Simplify the square root of [tex]\(9\)[/tex]:
Since [tex]\(\sqrt{9} = 3\)[/tex], we have:
[tex]\[
\sqrt{54} = 3 \sqrt{6}
\][/tex]
4. Multiply the simplified square root by the coefficient outside the square root:
[tex]\[
2 \sqrt{54} = 2 \times 3 \sqrt{6} = 6 \sqrt{6}
\][/tex]
Therefore, the expression [tex]\(2 \sqrt{54}\)[/tex] simplifies to:
[tex]\[
6 \sqrt{6}
\][/tex]
Numerically, [tex]\( \sqrt{6} \approx 2.449 \)[/tex]. Hence, multiplying by 6:
[tex]\[
6 \sqrt{6} \approx 6 \times 2.449 = 14.696938456699067
\][/tex]
So, the simplified and evaluated form of [tex]\(2 \sqrt{54}\)[/tex] is approximately [tex]\(14.696938456699067\)[/tex].
