Question

Combining radicals simplify the expression. Assume that all letters denote positive numbers.
\(\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}\)

Answer 1

Property of \(\displaystyle{\sqrt[{s}]{}}:\)
\(\displaystyle\sqrt{{{a}{b}}}=\sqrt{{a}}\sqrt{{b}}\)
Distributive property:
\(\displaystyle{a}{\left({b}+{c}\right)}={a}{b}+{a}{c}\)
Calculation:
Apply exponent rule simplify the expression,
\(\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}=\sqrt{{{2}^{4}\times{x}}}+\sqrt{{{x}^{4}\times{x}}}\)
\(\displaystyle=\sqrt{{{2}^{4}}}\times\sqrt{{x}}+\sqrt{{{x}^{4}}}\times\sqrt{{x}}\)
Using distributive property.
\(\displaystyle=\sqrt{{x}}\times{\left({2}^{{\frac{4}{{2}}}}+{x}^{{\frac{4}{{2}}}}\right)}\)
\(\displaystyle=\sqrt{{x}}\times{\left({4}+{x}^{2}\right)}\)
Answer: \(\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}=\sqrt{{x}}\times{\left({4}+{x}^{2}\right)}\)