Basic Math Examples

$\sqrt{\frac{32 y^{3}}{2 y}}$

Step 1

Reduce the expression $\frac{32 y^{3}}{2 y}$ by cancelling the common factors.

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Step 1.1

Factor $2$ out of $32 y^{3}$ .

$\sqrt{\frac{2 (16 y^{3})}{2 y}}$

Step 1.2

Factor $2$ out of $2 y$ .

$\sqrt{\frac{2 (16 y^{3})}{2 (y)}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{2 (16 y^{3})}{2 y}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{16 y^{3}}{y}}$

Step 2

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

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Step 2.1

Factor $y$ out of $16 y^{3}$ .

$\sqrt{\frac{y (16 y^{2})}{y}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Raise $y$ to the power of $1$ .

$\sqrt{\frac{y (16 y^{2})}{y^{1}}}$

Step 2.2.2

Factor $y$ out of $y^{1}$ .

$\sqrt{\frac{y (16 y^{2})}{y \cdot 1}}$

Step 2.2.3

Cancel the common factor.

$\sqrt{\frac{y (16 y^{2})}{y \cdot 1}}$

Step 2.2.4

Rewrite the expression.

$\sqrt{\frac{16 y^{2}}{1}}$

Step 2.2.5

Divide $16 y^{2}$ by $1$ .

$\sqrt{16 y^{2}}$

Step 3

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

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

Step 4

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

$4 y$