Sure! Let's simplify the expression [tex]\(\sqrt{3} \cdot \sqrt{30}\)[/tex] step-by-step.
1. Combine the square roots into a single square root:
[tex]\[
\sqrt{3} \cdot \sqrt{30} = \sqrt{3 \cdot 30}
\][/tex]
2. Multiply the numbers inside the square root:
[tex]\[
3 \cdot 30 = 90
\][/tex]
3. So, we have:
[tex]\[
\sqrt{3 \cdot 30} = \sqrt{90}
\][/tex]
The simplified form of [tex]\(\sqrt{3} \cdot \sqrt{30}\)[/tex] is [tex]\(\sqrt{90}\)[/tex].
4. Calculate the numerical value of [tex]\(\sqrt{90}\)[/tex]:
[tex]\[
\sqrt{90} \approx 9.486832980505138
\][/tex]
Thus:
[tex]\[
\sqrt{3} \cdot \sqrt{30} = \sqrt{90} \approx 9.486832980505138
\][/tex]
Therefore, the simplified product [tex]\(\sqrt{3} \cdot \sqrt{30}\)[/tex] is [tex]\(\sqrt{90}\)[/tex] and its approximate value is 9.486832980505138.
