Rationalize the Denominator (2 square root of 5x)/( square root of 7y^2)

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$\frac{2 \sqrt{5 x}}{\sqrt{7 y^{2}}}$

Simplify the denominator.

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Reorder $7$ and $y^{2}$ .

$\frac{2 \sqrt{5 x}}{\sqrt{y^{2} \cdot 7}}$

Pull terms out from under the radical.

$\frac{2 \sqrt{5 x}}{y \sqrt{7}}$

Multiply $\frac{2 \sqrt{5 x}}{y \sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{2 \sqrt{5 x}}{y \sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Combine and simplify the denominator.

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Multiply $\frac{2 \sqrt{5 x}}{y \sqrt{7}}$ and $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{2 \sqrt{5 x} \sqrt{7}}{y \sqrt{7} \sqrt{7}}$

Move $\sqrt{7}$ .

$\frac{2 \sqrt{5 x} \sqrt{7}}{y (\sqrt{7} \sqrt{7})}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{2 \sqrt{5 x} \sqrt{7}}{y ({\sqrt{7}}^{1} \sqrt{7})}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{2 \sqrt{5 x} \sqrt{7}}{y ({\sqrt{7}}^{1} {\sqrt{7}}^{1})}$

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

$\frac{2 \sqrt{5 x} \sqrt{7}}{y {\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{5 x} \sqrt{7}}{y {\sqrt{7}}^{2}}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{2 \sqrt{5 x} \sqrt{7}}{y {(7^{\frac{1}{2}})}^{2}}$

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

$\frac{2 \sqrt{5 x} \sqrt{7}}{y \cdot 7^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 \sqrt{5 x} \sqrt{7}}{y \cdot 7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 \sqrt{5 x} \sqrt{7}}{y \cdot 7^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{5 x} \sqrt{7}}{y \cdot 7^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{5 x} \sqrt{7}}{y \cdot 7}$

Simplify the numerator.

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Combine using the product rule for radicals.

$\frac{2 \sqrt{7 (5 x)}}{y \cdot 7}$

Multiply $7$ by $5$ .

$\frac{2 \sqrt{35 x}}{y \cdot 7}$

Move $7$ to the left of $y$ .

$\frac{2 \sqrt{35 x}}{7 y}$

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