Simplify square root of (6y^5)/(24y)

$\sqrt{\frac{6 y^{5}}{24 y}}$

Step 1

Reduce the expression $\frac{6 y^{5}}{24 y}$ by cancelling the common factors.

Factor $6$ out of $6 y^{5}$ .

$\sqrt{\frac{6 (y^{5})}{24 y}}$

Factor $6$ out of $24 y$ .

$\sqrt{\frac{6 (y^{5})}{6 (4 y)}}$

Cancel the common factor.

$\sqrt{\frac{6 y^{5}}{6 (4 y)}}$

Rewrite the expression.

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

Step 2

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

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

$\sqrt{\frac{y \cdot y^{4}}{4 y}}$

Cancel the common factors.

Factor $y$ out of $4 y$ .

$\sqrt{\frac{y \cdot y^{4}}{y \cdot 4}}$

Cancel the common factor.

$\sqrt{\frac{y \cdot y^{4}}{y \cdot 4}}$

Rewrite the expression.

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

Step 3

Simplify the expression.

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

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

Rewrite $4$ as $2^{2}$ .

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

Step 4

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

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

Step 5

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

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