Basic Math Examples

\sqrt{8 y^{3}} - \sqrt{72 y^{3}}

$\sqrt{8 y^{3}} - \sqrt{72 y^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

8 y^{3}

$8 y^{3}$ as

{(2 y)}^{2} \cdot (2 y)

${(2 y)}^{2} \cdot (2 y)$ .

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Step 1.1.1

Factor

4

$4$ out of

8

$8$ .

\sqrt{4 (2) y^{3}} - \sqrt{72 y^{3}}

$\sqrt{4 (2) y^{3}} - \sqrt{72 y^{3}}$

Step 1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\sqrt{2^{2} \cdot 2 y^{3}} - \sqrt{72 y^{3}}

$\sqrt{2^{2} \cdot 2 y^{3}} - \sqrt{72 y^{3}}$

Step 1.1.3

Factor out

y^{2}

$y^{2}$ .

\sqrt{2^{2} \cdot 2 (y^{2} y)} - \sqrt{72 y^{3}}

$\sqrt{2^{2} \cdot 2 (y^{2} y)} - \sqrt{72 y^{3}}$

Step 1.1.4

Move

2

$2$ .

\sqrt{2^{2} y^{2} \cdot 2 y} - \sqrt{72 y^{3}}

$\sqrt{2^{2} y^{2} \cdot 2 y} - \sqrt{72 y^{3}}$

Step 1.1.5

Rewrite

2^{2} y^{2}

$2^{2} y^{2}$ as

{(2 y)}^{2}

${(2 y)}^{2}$ .

\sqrt{{(2 y)}^{2} \cdot 2 y} - \sqrt{72 y^{3}}

$\sqrt{{(2 y)}^{2} \cdot 2 y} - \sqrt{72 y^{3}}$

Step 1.1.6

Add parentheses.

\sqrt{{(2 y)}^{2} \cdot (2 y)} - \sqrt{72 y^{3}}

$\sqrt{{(2 y)}^{2} \cdot (2 y)} - \sqrt{72 y^{3}}$

\sqrt{{(2 y)}^{2} \cdot (2 y)} - \sqrt{72 y^{3}}

$\sqrt{{(2 y)}^{2} \cdot (2 y)} - \sqrt{72 y^{3}}$

Step 1.2

Pull terms out from under the radical.

$2 y \sqrt{2 y} - \sqrt{72 y^{3}}$

Step 1.3

Rewrite

$72 y^{3}$ as

${(6 y)}^{2} \cdot (2 y)$ .

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Step 1.3.1

Factor

$36$ out of

$72$ .

$2 y \sqrt{2 y} - \sqrt{36 (2) y^{3}}$

Step 1.3.2

Rewrite

$36$ as

$6^{2}$ .

$2 y \sqrt{2 y} - \sqrt{6^{2} \cdot 2 y^{3}}$

Step 1.3.3

Factor out

$y^{2}$ .

$2 y \sqrt{2 y} - \sqrt{6^{2} \cdot 2 (y^{2} y)}$

Step 1.3.4

Move

$2$ .

$2 y \sqrt{2 y} - \sqrt{6^{2} y^{2} \cdot 2 y}$

Step 1.3.5

Rewrite

$6^{2} y^{2}$ as

${(6 y)}^{2}$ .

$2 y \sqrt{2 y} - \sqrt{{(6 y)}^{2} \cdot 2 y}$

Step 1.3.6

Add parentheses.

$2 y \sqrt{2 y} - \sqrt{{(6 y)}^{2} \cdot (2 y)}$

Step 1.4

Pull terms out from under the radical.

$2 y \sqrt{2 y} - (6 y \sqrt{2 y})$

Step 1.5

Multiply

$6$ by

$- 1$ .

$2 y \sqrt{2 y} - 6 y \sqrt{2 y}$

Step 2

Subtract

$6 y \sqrt{2 y}$ from

$2 y \sqrt{2 y}$ .

$- 4 y \sqrt{2 y}$