Simplify ( square root of 15x^4y^13)/( square root of 3x^3y^4)

$\frac{\sqrt{15 x^{4} y^{13}}}{\sqrt{3 x^{3} y^{4}}}$

Step 1

Combine $\sqrt{15 x^{4} y^{13}}$ and $\sqrt{3 x^{3} y^{4}}$ into a single radical.

$\sqrt{\frac{15 x^{4} y^{13}}{3 x^{3} y^{4}}}$

Step 2

Reduce the expression $\frac{15 x^{4} y^{13}}{3 x^{3} y^{4}}$ by cancelling the common factors.

Factor $3$ out of $15 x^{4} y^{13}$ .

$\sqrt{\frac{3 (5 x^{4} y^{13})}{3 x^{3} y^{4}}}$

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

$\sqrt{\frac{3 (5 x^{4} y^{13})}{3 (x^{3} y^{4})}}$

Cancel the common factor.

$\sqrt{\frac{3 (5 x^{4} y^{13})}{3 (x^{3} y^{4})}}$

Rewrite the expression.

$\sqrt{\frac{5 x^{4} y^{13}}{x^{3} y^{4}}}$

Step 3

Cancel the common factor of $x^{4}$ and $x^{3}$ .

Factor $x^{3}$ out of $5 x^{4} y^{13}$ .

$\sqrt{\frac{x^{3} (5 x y^{13})}{x^{3} y^{4}}}$

Cancel the common factors.

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

$\sqrt{\frac{x^{3} (5 x y^{13})}{x^{3} (y^{4})}}$

Cancel the common factor.

$\sqrt{\frac{x^{3} (5 x y^{13})}{x^{3} y^{4}}}$

Rewrite the expression.

$\sqrt{\frac{5 x y^{13}}{y^{4}}}$

Step 4

Cancel the common factor of $y^{13}$ and $y^{4}$ .

Factor $y^{4}$ out of $5 x y^{13}$ .

$\sqrt{\frac{y^{4} (5 x y^{9})}{y^{4}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{y^{4} (5 x y^{9})}{y^{4} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y^{4} (5 x y^{9})}{y^{4} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{5 x y^{9}}{1}}$

Divide $5 x y^{9}$ by $1$ .

$\sqrt{5 x y^{9}}$

Step 5

Rewrite $5 x y^{9}$ as ${({(y^{2})}^{2})}^{2} \cdot (5 x y)$ .

Factor out $y^{8}$ .

$\sqrt{5 x (y^{8} y)}$

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

$\sqrt{5 x ({(y^{4})}^{2} y)}$

Move $x$ .

$\sqrt{5 {(y^{4})}^{2} x y}$

Reorder $5$ and ${(y^{4})}^{2}$ .

$\sqrt{{(y^{4})}^{2} \cdot 5 x y}$

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

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

Add parentheses.

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply the exponents in ${(y^{2})}^{2}$ .

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

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

Multiply $2$ by $2$ .

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

Simplify ( square root of 15x^4y^13)/( square root of 3x^3y^4)

Related Questions

Support LCMGCF.com by disabling your adblocker.