Simplify square root of 2x(7+ square root of 2x)

$\sqrt{2 x} (7 + \sqrt{2 x})$

Step 1

Apply the distributive property.

$\sqrt{2 x} \cdot 7 + \sqrt{2 x} \sqrt{2 x}$

Step 2

Move $7$ to the left of $\sqrt{2 x}$ .

$7 \cdot \sqrt{2 x} + \sqrt{2 x} \sqrt{2 x}$

Step 3

Multiply $\sqrt{2 x} \sqrt{2 x}$ .

Raise $\sqrt{2 x}$ to the power of $1$ .

$7 \cdot \sqrt{2 x} + {\sqrt{2 x}}^{1} \sqrt{2 x}$

Raise $\sqrt{2 x}$ to the power of $1$ .

$7 \cdot \sqrt{2 x} + {\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 \cdot \sqrt{2 x} + {\sqrt{2 x}}^{1 + 1}$

Add $1$ and $1$ .

$7 \cdot \sqrt{2 x} + {\sqrt{2 x}}^{2}$

Step 4

Rewrite ${\sqrt{2 x}}^{2}$ as $2 x$ .

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

$7 \sqrt{2 x} + {({(2 x)}^{\frac{1}{2}})}^{2}$

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

$7 \sqrt{2 x} + {(2 x)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$7 \sqrt{2 x} + {(2 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$7 \sqrt{2 x} + {(2 x)}^{\frac{2}{2}}$

Rewrite the expression.

$7 \sqrt{2 x} + {(2 x)}^{1}$

Simplify.

$7 \sqrt{2 x} + 2 x$