Certainly! Let's solve the expression [tex]\(-7 \cdot \sqrt{200}\)[/tex] step by step.
1. Determine the value of [tex]\(\sqrt{200}\)[/tex]:
- The square root of 200 is approximately [tex]\(14.142135623730951\)[/tex].
2. Multiply [tex]\(-7\)[/tex] by the square root of 200:
- Given that [tex]\(\sqrt{200} \approx 14.142135623730951\)[/tex], we can now multiply:
[tex]\[
-7 \cdot 14.142135623730951
\][/tex]
3. Perform the multiplication:
- [tex]\(-7 \cdot 14.142135623730951\)[/tex] equals approximately [tex]\(-98.99494936611666\)[/tex].
Thus, the detailed solution for the expression [tex]\(-7 \cdot \sqrt{200}\)[/tex] is:
[tex]\[
\sqrt{200} \approx 14.142135623730951
\][/tex]
[tex]\[
-7 \cdot 14.142135623730951 \approx -98.99494936611666
\][/tex]
Therefore, [tex]\(-7 \cdot \sqrt{200} \approx -98.99494936611666\)[/tex].
