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. displaystylesqrt{{{16}{x}}}+sqrt{{{x}^{5}}}

Bergen 2021-02-08 Answered

Combining radicals simplify the expression. Assume that all letters denote positive numbers.

\sqrt{16 x} + \sqrt{x^{5}}

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Expert Answer

broliY

Answered 2021-02-09 Author has 97 answers

Property of

\sqrt[s]{} :

\sqrt{a b} = \sqrt{a} \sqrt{b}

Distributive property:

a (b + c) = a b + a c

Calculation:
Apply exponent rule simplify the expression,

\sqrt{16 x} + \sqrt{x^{5}} = \sqrt{2^{4} \times x} + \sqrt{x^{4} \times x}

= \sqrt{2^{4}} \times \sqrt{x} + \sqrt{x^{4}} \times \sqrt{x}

Using distributive property.

= \sqrt{x} \times (2^{\frac{4}{2}} + x^{\frac{4}{2}})

= \sqrt{x} \times (4 + x^{2})

Answer:

\sqrt{16 x} + \sqrt{x^{5}} = \sqrt{x} \times (4 + x^{2})

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Jeffrey Jordon

Answered 2021-10-25 Author has 2027 answers

Answer is given below (on video)

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