Basic Math Examples

$y \sqrt{112 y} + 4 \sqrt{175 y^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $112 y$ as ${(2^{2})}^{2} \cdot (7 y)$ .

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Step 1.1.1

Factor $16$ out of $112$ .

$y \sqrt{16 (7) y} + 4 \sqrt{175 y^{3}}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$y \sqrt{4^{2} \cdot 7 y} + 4 \sqrt{175 y^{3}}$

Step 1.1.3

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

$y \sqrt{{(2^{2})}^{2} \cdot 7 y} + 4 \sqrt{175 y^{3}}$

Step 1.1.4

Add parentheses.

$y \sqrt{{(2^{2})}^{2} \cdot (7 y)} + 4 \sqrt{175 y^{3}}$

Step 1.2

Pull terms out from under the radical.

$y (2^{2} \sqrt{7 y}) + 4 \sqrt{175 y^{3}}$

Step 1.3

Rewrite using the commutative property of multiplication.

$2^{2} y \sqrt{7 y} + 4 \sqrt{175 y^{3}}$

Step 1.4

Raise $2$ to the power of $2$ .

$4 y \sqrt{7 y} + 4 \sqrt{175 y^{3}}$

Step 1.5

Rewrite $175 y^{3}$ as ${(5 y)}^{2} \cdot (7 y)$ .

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Step 1.5.1

Factor $25$ out of $175$ .

$4 y \sqrt{7 y} + 4 \sqrt{25 (7) y^{3}}$

Step 1.5.2

Rewrite $25$ as $5^{2}$ .

$4 y \sqrt{7 y} + 4 \sqrt{5^{2} \cdot 7 y^{3}}$

Step 1.5.3

Factor out $y^{2}$ .

$4 y \sqrt{7 y} + 4 \sqrt{5^{2} \cdot 7 (y^{2} y)}$

Step 1.5.4

Move $7$ .

$4 y \sqrt{7 y} + 4 \sqrt{5^{2} y^{2} \cdot 7 y}$

Step 1.5.5

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

$4 y \sqrt{7 y} + 4 \sqrt{{(5 y)}^{2} \cdot 7 y}$

Step 1.5.6

Add parentheses.

$4 y \sqrt{7 y} + 4 \sqrt{{(5 y)}^{2} \cdot (7 y)}$

Step 1.6

Pull terms out from under the radical.

$4 y \sqrt{7 y} + 4 (5 y \sqrt{7 y})$

Step 1.7

Multiply $5$ by $4$ .

$4 y \sqrt{7 y} + 20 y \sqrt{7 y}$

Step 2

Add $4 y \sqrt{7 y}$ and $20 y \sqrt{7 y}$ .

$24 y \sqrt{7 y}$