To solve for the value of [tex]\( 7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}} \)[/tex], let's proceed with the following steps:
1. Calculate [tex]\( 7^{\frac{1}{2}} \)[/tex]:
- The term [tex]\( 7^{\frac{1}{2}} \)[/tex] represents the square root of 7.
- Numerically, [tex]\( 7^{\frac{1}{2}} \approx 2.6457513110645907 \)[/tex].
2. Calculate [tex]\( 8^{\frac{1}{2}} \)[/tex]:
- The term [tex]\( 8^{\frac{1}{2}} \)[/tex] represents the square root of 8.
- Numerically, [tex]\( 8^{\frac{1}{2}} \approx 2.8284271247461903 \)[/tex].
3. Multiply the results:
- We now multiply the two terms obtained:
[tex]\[
2.6457513110645907 \cdot 2.8284271247461903
\][/tex]
- Performing the multiplication, we get:
[tex]\[
2.6457513110645907 \times 2.8284271247461903 \approx 7.4833147735478835
\][/tex]
Therefore, the value of [tex]\( 7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}} \)[/tex] is approximately [tex]\( 7.4833147735478835 \)[/tex].
