Simplify ( square root of 3x^12y^10)/(5x^6y^3)

$\frac{\sqrt{3 x^{12} y^{10}}}{5 x^{6} y^{3}}$

Step 1

Simplify the numerator.

Rewrite $3 x^{12} y^{10}$ as ${(x^{6} y^{5})}^{2} \cdot 3$ .

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

$\frac{\sqrt{3 {(x^{6})}^{2} y^{10}}}{5 x^{6} y^{3}}$

Rewrite $y^{10}$ as ${(y^{5})}^{2}$ .

$\frac{\sqrt{3 {(x^{6})}^{2} {(y^{5})}^{2}}}{5 x^{6} y^{3}}$

Move $3$ .

$\frac{\sqrt{{(x^{6})}^{2} {(y^{5})}^{2} \cdot 3}}{5 x^{6} y^{3}}$

Rewrite ${(x^{6})}^{2} {(y^{5})}^{2}$ as ${(x^{6} y^{5})}^{2}$ .

$\frac{\sqrt{{(x^{6} y^{5})}^{2} \cdot 3}}{5 x^{6} y^{3}}$

Pull terms out from under the radical.

$\frac{x^{6} y^{5} \sqrt{3}}{5 x^{6} y^{3}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{6}$ .

Cancel the common factor.

$\frac{x^{6} y^{5} \sqrt{3}}{5 x^{6} y^{3}}$

Rewrite the expression.

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

Cancel the common factor of $y^{5}$ and $y^{3}$ .

Factor $y^{3}$ out of $y^{5} \sqrt{3}$ .

$\frac{y^{3} (y^{2} \sqrt{3})}{5 y^{3}}$

Cancel the common factors.

Factor $y^{3}$ out of $5 y^{3}$ .

$\frac{y^{3} (y^{2} \sqrt{3})}{y^{3} \cdot 5}$

Cancel the common factor.

$\frac{y^{3} (y^{2} \sqrt{3})}{y^{3} \cdot 5}$

Rewrite the expression.

$\frac{y^{2} \sqrt{3}}{5}$