Basic Math Examples

$\sqrt{20 w^{2} u^{3}} \sqrt{5 w^{7} u}$

Step 1

Rewrite $20 w^{2} u^{3}$ as ${(2 w u)}^{2} \cdot (5 u)$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $20$ .

$\sqrt{4 (5) w^{2} u^{3}} \sqrt{5 w^{7} u}$

Step 1.2

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

$\sqrt{2^{2} \cdot 5 w^{2} u^{3}} \sqrt{5 w^{7} u}$

Step 1.3

Factor out $u^{2}$ .

$\sqrt{2^{2} \cdot 5 w^{2} (u^{2} u)} \sqrt{5 w^{7} u}$

Step 1.4

Move $5$ .

$\sqrt{2^{2} w^{2} u^{2} \cdot 5 u} \sqrt{5 w^{7} u}$

Step 1.5

Rewrite $2^{2} w^{2} u^{2}$ as ${(2 w u)}^{2}$ .

$\sqrt{{(2 w u)}^{2} \cdot 5 u} \sqrt{5 w^{7} u}$

Step 1.6

Add parentheses.

$\sqrt{{(2 w u)}^{2} \cdot (5 u)} \sqrt{5 w^{7} u}$

Step 2

Pull terms out from under the radical.

$2 w u \sqrt{5 u} \sqrt{5 w^{7} u}$

Step 3

Rewrite $5 w^{7} u$ as ${(w^{3})}^{2} \cdot (5 w u)$ .

Tap for more steps...

Step 3.1

Factor out $w^{6}$ .

$2 w u \sqrt{5 u} \sqrt{5 (w^{6} w) u}$

Step 3.2

Rewrite $w^{6}$ as ${(w^{3})}^{2}$ .

$2 w u \sqrt{5 u} \sqrt{5 ({(w^{3})}^{2} w) u}$

Step 3.3

Reorder $5$ and ${(w^{3})}^{2}$ .

$2 w u \sqrt{5 u} \sqrt{{(w^{3})}^{2} \cdot 5 w u}$

Step 3.4

Add parentheses.

$2 w u \sqrt{5 u} \sqrt{{(w^{3})}^{2} \cdot 5 (w u)}$

Step 3.5

Add parentheses.

$2 w u \sqrt{5 u} \sqrt{{(w^{3})}^{2} \cdot (5 w u)}$

Step 4

Pull terms out from under the radical.

$2 w u \sqrt{5 u} (w^{3} \sqrt{5 w u})$

Step 5

Multiply $w$ by $w^{3}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $w^{3}$ .

$2 (w^{3} w) u \sqrt{5 u} \sqrt{5 w u}$

Step 5.2

Multiply $w^{3}$ by $w$ .

Tap for more steps...

Step 5.2.1

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

$2 (w^{3} w^{1}) u \sqrt{5 u} \sqrt{5 w u}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 w^{3 + 1} u \sqrt{5 u} \sqrt{5 w u}$

Step 5.3

Add $3$ and $1$ .

$2 w^{4} u \sqrt{5 u} \sqrt{5 w u}$

Step 6

Multiply $2 w^{4} u \sqrt{5 u} \sqrt{5 w u}$ .

Tap for more steps...

Step 6.1

Combine using the product rule for radicals.

$2 w^{4} u \sqrt{5 w u (5 u)}$

Step 6.2

Multiply $5$ by $5$ .

$2 w^{4} u \sqrt{25 w u \cdot u}$

Step 6.3

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

$2 w^{4} u \sqrt{25 w (u^{1} u)}$

Step 6.4

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

$2 w^{4} u \sqrt{25 w (u^{1} u^{1})}$

Step 6.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 w^{4} u \sqrt{25 w u^{1 + 1}}$

Step 6.6

Add $1$ and $1$ .

$2 w^{4} u \sqrt{25 w u^{2}}$

Step 7

Rewrite $25 w u^{2}$ as ${(5 u)}^{2} w$ .

Tap for more steps...

Step 7.1

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

$2 w^{4} u \sqrt{5^{2} w u^{2}}$

Step 7.2

Move $w$ .

$2 w^{4} u \sqrt{5^{2} u^{2} w}$

Step 7.3

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

$2 w^{4} u \sqrt{{(5 u)}^{2} w}$

Step 8

Pull terms out from under the radical.

$2 w^{4} u (5 u \sqrt{w})$

Step 9

Multiply $u$ by $u$ by adding the exponents.

Tap for more steps...

Step 9.1

Move $u$ .

$2 w^{4} (u \cdot u) (5 \sqrt{w})$

Step 9.2

Multiply $u$ by $u$ .

$2 w^{4} u^{2} (5 \sqrt{w})$

Step 10

Multiply $5$ by $2$ .

$10 w^{4} u^{2} \sqrt{w}$