# Combining radicals simplify the expression. Assume that all letters denote positive numbers. displaystylesqrt{{{16}{x}}}+sqrt{{{x}^{5}}}

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

2021-02-09
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: $$\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}=\sqrt{{x}}\times{\left({4}+{x}^{2}\right)}$$

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