Simplify ( square root of 8x^2)÷( square root of 3x)

$\sqrt{8 x^{2}} \div \sqrt{3 x}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{8 x^{2}}}{\sqrt{3 x}}$

Step 2

Combine $\sqrt{8 x^{2}}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{8 x^{2}}{3 x}}$

Step 3

Reduce the expression $\frac{8 x^{2}}{3 x}$ by cancelling the common factors.

Factor $x$ out of $8 x^{2}$ .

$\sqrt{\frac{x (8 x)}{3 x}}$

Factor $x$ out of $3 x$ .

$\sqrt{\frac{x (8 x)}{x \cdot 3}}$

Cancel the common factor.

$\sqrt{\frac{x (8 x)}{x \cdot 3}}$

Rewrite the expression.

$\sqrt{\frac{8 x}{3}}$

Step 4

Rewrite $\sqrt{\frac{8 x}{3}}$ as $\frac{\sqrt{8 x}}{\sqrt{3}}$ .

$\frac{\sqrt{8 x}}{\sqrt{3}}$

Step 5

Simplify the numerator.

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2) x}}{\sqrt{3}}$

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

$\frac{\sqrt{2^{2} \cdot 2 x}}{\sqrt{3}}$

Add parentheses.

$\frac{\sqrt{2^{2} \cdot (2 x)}}{\sqrt{3}}$

Pull terms out from under the radical.

$\frac{2 \sqrt{2 x}}{\sqrt{3}}$

Step 6

Multiply $\frac{2 \sqrt{2 x}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{2 \sqrt{2 x}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 7

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{2 x}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{2 \sqrt{2 x} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{2 \sqrt{2 x} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{2 \sqrt{2 x} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$\frac{2 \sqrt{2 x} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{2 x} \sqrt{3}}{{\sqrt{3}}^{2}}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{2 \sqrt{2 x} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

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

$\frac{2 \sqrt{2 x} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 \sqrt{2 x} \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{2 x} \sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{2 x} \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{2 x} \sqrt{3}}{3}$

Step 8

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{2 \sqrt{3 (2 x)}}{3}$

Multiply $3$ by $2$ .

$\frac{2 \sqrt{6 x}}{3}$

Simplify ( square root of 8x^2)÷( square root of 3x)

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