Pre-Algebra Examples

$\sqrt{25 x + \sqrt{16 x}}$

Step 1

Simplify the expression.

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{16 x}$ as ${(16 x)}^{\frac{1}{2}}$ .

$\sqrt{25 x + {(16 x)}^{\frac{1}{2}}}$

Step 1.2

Apply the product rule to $16 x$ .

$\sqrt{25 x + 16^{\frac{1}{2}} x^{\frac{1}{2}}}$

Step 1.3

Rewrite $16$ as $4^{2}$ .

$\sqrt{25 x + {(4^{2})}^{\frac{1}{2}} x^{\frac{1}{2}}}$

Step 1.4

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{25 x + 4^{2 (\frac{1}{2})} x^{\frac{1}{2}}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\sqrt{25 x + 4^{2 (\frac{1}{2})} x^{\frac{1}{2}}}$

Step 2.2

Rewrite the expression.

$\sqrt{25 x + 4^{1} x^{\frac{1}{2}}}$

Step 3

Evaluate the exponent.

$\sqrt{25 x + 4 x^{\frac{1}{2}}}$

Step 4

Factor $x^{\frac{1}{2}}$ out of $25 x + 4 x^{\frac{1}{2}}$ .

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Step 4.1

Factor $x^{\frac{1}{2}}$ out of $25 x$ .

$\sqrt{x^{\frac{1}{2}} (25 x^{\frac{1}{2}}) + 4 x^{\frac{1}{2}}}$

Step 4.2

Factor $x^{\frac{1}{2}}$ out of $4 x^{\frac{1}{2}}$ .

$\sqrt{x^{\frac{1}{2}} (25 x^{\frac{1}{2}}) + x^{\frac{1}{2}} \cdot 4}$

Step 4.3

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{1}{2}} (25 x^{\frac{1}{2}}) + x^{\frac{1}{2}} \cdot 4$ .

$\sqrt{x^{\frac{1}{2}} (25 x^{\frac{1}{2}} + 4)}$