Simplify ( square root of 7x^5y)÷( square root of 28xy^3)

$\sqrt{7 x^{5} y} \div \sqrt{28 x y^{3}}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{7 x^{5} y}}{\sqrt{28 x y^{3}}}$

Step 2

Combine $\sqrt{7 x^{5} y}$ and $\sqrt{28 x y^{3}}$ into a single radical.

$\sqrt{\frac{7 x^{5} y}{28 x y^{3}}}$

Step 3

Reduce the expression $\frac{7 x^{5} y}{28 x y^{3}}$ by cancelling the common factors.

Factor $7$ out of $7 x^{5} y$ .

$\sqrt{\frac{7 (x^{5} y)}{28 x y^{3}}}$

Factor $7$ out of $28 x y^{3}$ .

$\sqrt{\frac{7 (x^{5} y)}{7 (4 x y^{3})}}$

Cancel the common factor.

$\sqrt{\frac{7 (x^{5} y)}{7 (4 x y^{3})}}$

Rewrite the expression.

$\sqrt{\frac{x^{5} y}{4 x y^{3}}}$

Step 4

Cancel the common factor of $x^{5}$ and $x$ .

Factor $x$ out of $x^{5} y$ .

$\sqrt{\frac{x (x^{4} y)}{4 x y^{3}}}$

Cancel the common factors.

Factor $x$ out of $4 x y^{3}$ .

$\sqrt{\frac{x (x^{4} y)}{x (4 y^{3})}}$

Cancel the common factor.

$\sqrt{\frac{x (x^{4} y)}{x (4 y^{3})}}$

Rewrite the expression.

$\sqrt{\frac{x^{4} y}{4 y^{3}}}$

Step 5

Cancel the common factor of $y$ and $y^{3}$ .

Factor $y$ out of $x^{4} y$ .

$\sqrt{\frac{y x^{4}}{4 y^{3}}}$

Cancel the common factors.

Factor $y$ out of $4 y^{3}$ .

$\sqrt{\frac{y x^{4}}{y (4 y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{y x^{4}}{y (4 y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{x^{4}}{4 y^{2}}}$

Step 6

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{\frac{{(x^{2})}^{2}}{4 y^{2}}}$

Step 7

Rewrite $4 y^{2}$ as ${(2 y)}^{2}$ .

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

Step 8

Rewrite $\frac{{(x^{2})}^{2}}{{(2 y)}^{2}}$ as ${(\frac{x^{2}}{2 y})}^{2}$ .

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

Step 9

Pull terms out from under the radical, assuming positive real numbers.

$\frac{x^{2}}{2 y}$

Simplify ( square root of 7x^5y)÷( square root of 28xy^3)

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