Bergen

2021-02-08

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

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

broliY

Skilled2021-02-09Added 97 answers

Property of $\sqrt[s]{}:$

$\sqrt{ab}=\sqrt{a}\sqrt{b}$

Distributive property:

$a(b+c)=ab+ac$

Calculation:

Apply exponent rule simplify the expression,

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

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

Using distributive property.

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

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

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

Distributive property:

Calculation:

Apply exponent rule simplify the expression,

Using distributive property.

Answer:

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

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