Certainly! Let's solve the expression [tex]\(\frac{\sqrt{21} \times \sqrt{28}}{\sqrt{121}}\)[/tex] step-by-step.
1. Identify the components of the expression:
- Numerator: [tex]\(\sqrt{21} \times \sqrt{28}\)[/tex]
- Denominator: [tex]\(\sqrt{121}\)[/tex]
2. Simplify the numerator:
To simplify [tex]\(\sqrt{21} \times \sqrt{28}\)[/tex], we use the property of square roots that states [tex]\(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\)[/tex]. So:
[tex]\[
\sqrt{21} \times \sqrt{28} = \sqrt{21 \times 28}
\][/tex]
3. Calculate the product inside the square root:
[tex]\[
21 \times 28 = 588
\][/tex]
So the expression becomes:
[tex]\[
\frac{\sqrt{588}}{\sqrt{121}}
\][/tex]
4. Simplify the denominator:
The denominator is [tex]\(\sqrt{121}\)[/tex], and since [tex]\(121\)[/tex] is a perfect square:
[tex]\[
\sqrt{121} = 11
\][/tex]
5. Substitute the values back into the expression:
We now have:
[tex]\[
\frac{\sqrt{588}}{11}
\][/tex]
6. Evaluate the square root in the numerator:
The square root of [tex]\(588\)[/tex] approximately equals [tex]\(24.24871130596428\)[/tex] (obtaining this value from a reliable source such as a calculator).
7. Perform the division:
Divide the evaluated numerator by the simplified denominator:
[tex]\[
\frac{24.24871130596428}{11} \approx 2.2044283005422076
\][/tex]
Therefore, the final result of the given expression [tex]\(\frac{\sqrt{21} \times \sqrt{28}}{\sqrt{121}}\)[/tex] is approximately [tex]\(2.2044283005422076\)[/tex].
