Question

simplify the expression shown below.
\\(\sqrt{5}\left(\sqrt8{5}\
ight)\\)
\\(\sqrt{5}\left(\sqrt8{5}\
ight) = \square\\)
(simplify your answer, including any radicals. use integers or fract

Explanation:

Step1: Convert radicals to exponents

$\sqrt{5} = 5^{\frac{1}{2}}$, $\sqrt[8]{5} = 5^{\frac{1}{8}}$

Step2: Multiply using exponent rule

When multiplying like bases, add exponents: $5^{\frac{1}{2}} \times 5^{\frac{1}{8}} = 5^{\frac{1}{2}+\frac{1}{8}}$

Step3: Add the fractions

$\frac{1}{2}+\frac{1}{8} = \frac{4}{8}+\frac{1}{8} = \frac{5}{8}$

Step4: Convert back to radical form

$5^{\frac{5}{8}} = \sqrt[8]{5^5}$

Step5: Simplify the radicand

$5^5 = 3125$, so $\sqrt[8]{3125}$

Answer:

$\sqrt[8]{3125}$ (or $5^{\frac{5}{8}}$)