To simplify the expression [tex]\(\sqrt{5} \cdot \sqrt{7}\)[/tex], we can use the property of square roots that states:
[tex]\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\][/tex]
Applying this property to our expression:
[tex]\[
\sqrt{5} \cdot \sqrt{7} = \sqrt{5 \cdot 7}
\][/tex]
Next, we multiply the numbers under the square root:
[tex]\[
5 \cdot 7 = 35
\][/tex]
So, our expression simplifies to:
[tex]\[
\sqrt{35}
\][/tex]
Therefore, the simplified expression is:
[tex]\[
\sqrt{35}
\][/tex]
In addition to the simplified radical form, we can also approximate the numerical value of [tex]\(\sqrt{35}\)[/tex]. Using a calculator or other methods to find the square root of 35, we get:
[tex]\[
\sqrt{35} \approx 5.916
\][/tex]
Thus, [tex]\(\sqrt{5} \cdot \sqrt{7}\)[/tex] simplifies to [tex]\(\sqrt{35}\)[/tex], which is approximately 5.916 when evaluated numerically.
