Certainly! Let's work through the expressions step by step:
1. Calculating the fifth root of 8:
The fifth root of a number is the value which, when multiplied by itself five times, gives that number. The fifth root of 8 can be found by solving the equation [tex]\( x^5 = 8 \)[/tex].
Mathematically, this is expressed as:
[tex]\[
\sqrt[5]{8} = 8^{1/5}
\][/tex]
Evaluating [tex]\( 8^{1/5} \)[/tex] gives us approximately:
[tex]\[
\sqrt[5]{8} \approx 1.5157
\][/tex]
Thus, the fifth root of 8 is approximately 1.5157.
2. Calculating 8 times the square root of 5:
The square root of a number is the value which, when multiplied by itself, gives that number. The square root of 5 can be found by solving the equation [tex]\( y^2 = 5 \)[/tex].
Mathematically, this is expressed as:
[tex]\[
\sqrt{5} = 5^{1/2}
\][/tex]
Evaluating [tex]\( 5^{1/2} \)[/tex] gives us approximately:
[tex]\[
\sqrt{5} \approx 2.2361
\][/tex]
Next, we need to multiply this result by 8:
[tex]\[
8 \times \sqrt{5} = 8 \times 2.2361 \approx 17.8885
\][/tex]
So, 8 times the square root of 5 is approximately 17.8885.
In summary, the detailed calculations yield:
1. The fifth root of 8 is approximately 1.5157.
2. 8 times the square root of 5 is approximately 17.8885.
