Basic Math Examples

$w \sqrt{32 v^{3}} + 7 \sqrt{\sqrt{50 v w}}$

Step 1

Rewrite $32 v^{3}$ as ${(4 v)}^{2} \cdot (2 v)$ .

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Step 1.1

Factor $16$ out of $32$ .

$w \sqrt{16 (2) v^{3}} + 7 \sqrt{\sqrt{50 v w}}$

Step 1.2

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

$w \sqrt{4^{2} \cdot 2 v^{3}} + 7 \sqrt{\sqrt{50 v w}}$

Step 1.3

Factor out $v^{2}$ .

$w \sqrt{4^{2} \cdot 2 (v^{2} v)} + 7 \sqrt{\sqrt{50 v w}}$

Step 1.4

Move $2$ .

$w \sqrt{4^{2} v^{2} \cdot 2 v} + 7 \sqrt{\sqrt{50 v w}}$

Step 1.5

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

$w \sqrt{{(4 v)}^{2} \cdot 2 v} + 7 \sqrt{\sqrt{50 v w}}$

Step 1.6

Add parentheses.

$w \sqrt{{(4 v)}^{2} \cdot (2 v)} + 7 \sqrt{\sqrt{50 v w}}$

Step 2

Pull terms out from under the radical.

$w (4 v \sqrt{2 v}) + 7 \sqrt{\sqrt{50 v w}}$

Step 3

Rewrite using the commutative property of multiplication.

$4 w v \sqrt{2 v} + 7 \sqrt{\sqrt{50 v w}}$

Step 4

Rewrite $50 v w$ as $5^{2} \cdot (2 v w)$ .

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Step 4.1

Factor $25$ out of $50$ .

$4 w v \sqrt{2 v} + 7 \sqrt{\sqrt{25 (2) v w}}$

Step 4.2

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

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

Step 4.3

Add parentheses.

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

Step 4.4

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$4 w v \sqrt{2 v} + 7 \sqrt{5 \sqrt{2 v w}}$