Simplify the Radical Expression square root of (7x)/(10y^3)

$\sqrt{\frac{7 x}{10 y^{3}}}$

Step 1

Rewrite $\frac{7 x}{10 y^{3}}$ as ${(\frac{1}{y})}^{2} \frac{7 x}{10 y}$ .

Factor the perfect power $1^{2}$ out of $7 x$ .

$\sqrt{\frac{1^{2} (7 x)}{10 y^{3}}}$

Factor the perfect power $y^{2}$ out of $10 y^{3}$ .

$\sqrt{\frac{1^{2} (7 x)}{y^{2} \cdot (10 y)}}$

Rearrange the fraction $\frac{1^{2} (7 x)}{y^{2} \cdot (10 y)}$ .

$\sqrt{{(\frac{1}{y})}^{2} \frac{7 x}{10 y}}$

Step 2

Pull terms out from under the radical.

$| \frac{1}{y} | \sqrt{\frac{7 x}{10 y}}$

Step 3

Rewrite $\sqrt{\frac{7 x}{10 y}}$ as $\frac{\sqrt{7 x}}{\sqrt{10 y}}$ .

$| \frac{1}{y} | \frac{\sqrt{7 x}}{\sqrt{10 y}}$

Step 4

Multiply $\frac{\sqrt{7 x}}{\sqrt{10 y}}$ by $\frac{\sqrt{10 y}}{\sqrt{10 y}}$ .

$| \frac{1}{y} | (\frac{\sqrt{7 x}}{\sqrt{10 y}} \cdot \frac{\sqrt{10 y}}{\sqrt{10 y}})$

Step 5

Combine and simplify the denominator.

Multiply $\frac{\sqrt{7 x}}{\sqrt{10 y}}$ by $\frac{\sqrt{10 y}}{\sqrt{10 y}}$ .

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{\sqrt{10 y} \sqrt{10 y}}$

Raise $\sqrt{10 y}$ to the power of $1$ .

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{\sqrt{10 y}}^{1} \sqrt{10 y}}$

Raise $\sqrt{10 y}$ to the power of $1$ .

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{\sqrt{10 y}}^{1} {\sqrt{10 y}}^{1}}$

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

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{\sqrt{10 y}}^{1 + 1}}$

Add $1$ and $1$ .

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{\sqrt{10 y}}^{2}}$

Rewrite ${\sqrt{10 y}}^{2}$ as $10 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 y}$ as ${(10 y)}^{\frac{1}{2}}$ .

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{({(10 y)}^{\frac{1}{2}})}^{2}}$

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

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{(10 y)}^{\frac{1}{2} \cdot 2}}$

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

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{(10 y)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{(10 y)}^{\frac{2}{2}}}$

Rewrite the expression.

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{{(10 y)}^{1}}$

Simplify.

$| \frac{1}{y} | \frac{\sqrt{7 x} \sqrt{10 y}}{10 y}$

Step 6

Simplify the numerator.

Combine using the product rule for radicals.

$| \frac{1}{y} | \frac{\sqrt{7 x (10 y)}}{10 y}$

Multiply $10$ by $7$ .

$| \frac{1}{y} | \frac{\sqrt{70 x y}}{10 y}$

Step 7

Combine $| \frac{1}{y} |$ and $\frac{\sqrt{70 x y}}{10 y}$ .

$\frac{| \frac{1}{y} | \sqrt{70 x y}}{10 y}$

Simplify the Radical Expression square root of (7x)/(10y^3)

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