To solve the expression [tex]\(\sqrt{3}(\sqrt{12} + \sqrt{8})\)[/tex], we will break it down step by step.
1. Calculate each square root term separately:
[tex]\(\sqrt{3}\)[/tex]
The square root of 3 is approximately [tex]\(1.7320508075688772\)[/tex].
[tex]\(\sqrt{12}\)[/tex]
The square root of 12 is approximately [tex]\(3.4641016151377544\)[/tex].
[tex]\(\sqrt{8}\)[/tex]
The square root of 8 is approximately [tex]\(2.8284271247461903\)[/tex].
2. Calculate the inner sum:
Add [tex]\(\sqrt{12}\)[/tex] and [tex]\(\sqrt{8}\)[/tex]:
[tex]\[
\sqrt{12} + \sqrt{8} = 3.4641016151377544 + 2.8284271247461903 = 6.292528739883945
\][/tex]
3. Calculate the final product:
Multiply [tex]\(\sqrt{3}\)[/tex] by the sum of [tex]\(\sqrt{12}\)[/tex] and [tex]\(\sqrt{8}\)[/tex]:
[tex]\[
\sqrt{3} \times (\sqrt{12} + \sqrt{8}) = 1.7320508075688772 \times 6.292528739883945 = 10.898979485566356
\][/tex]
So, the value of the expression [tex]\(\sqrt{3}(\sqrt{12} + \sqrt{8})\)[/tex] is approximately [tex]\(10.898979485566356\)[/tex].
