 # Combining radicals simplify the expression. Assume that all letters denote positive numbers. displaystylesqrt{{{16}{x}}}+sqrt{{{x}^{5}}} Bergen 2021-02-08 Answered
Combining radicals simplify the expression. Assume that all letters denote positive numbers.
$\sqrt{16x}+\sqrt{{x}^{5}}$
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Property of $\sqrt[s]{}:$
$\sqrt{ab}=\sqrt{a}\sqrt{b}$
Distributive property:
$a\left(b+c\right)=ab+ac$
Calculation:
Apply exponent rule simplify the expression,
$\sqrt{16x}+\sqrt{{x}^{5}}=\sqrt{{2}^{4}×x}+\sqrt{{x}^{4}×x}$
$=\sqrt{{2}^{4}}×\sqrt{x}+\sqrt{{x}^{4}}×\sqrt{x}$
Using distributive property.
$=\sqrt{x}×\left({2}^{\frac{4}{2}}+{x}^{\frac{4}{2}}\right)$
$=\sqrt{x}×\left(4+{x}^{2}\right)$
Answer: $\sqrt{16x}+\sqrt{{x}^{5}}=\sqrt{x}×\left(4+{x}^{2}\right)$
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