Finite Math Examples

$2 \sqrt{15 a b} \cdot (3 \sqrt{21 a b^{3}})$

Step 1

Rewrite $21 a b^{3}$ as $b^{2} \cdot (21 a b)$ .

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Step 1.1

Factor out $b^{2}$ .

$2 \sqrt{15 a b} \cdot (3 \sqrt{21 a (b^{2} b)})$

Step 1.2

Move $a$ .

$2 \sqrt{15 a b} \cdot (3 \sqrt{21 b^{2} a b})$

Step 1.3

Reorder $21$ and $b^{2}$ .

$2 \sqrt{15 a b} \cdot (3 \sqrt{b^{2} \cdot 21 a b})$

Step 1.4

Add parentheses.

$2 \sqrt{15 a b} \cdot (3 \sqrt{b^{2} \cdot 21 (a b)})$

Step 1.5

Add parentheses.

$2 \sqrt{15 a b} \cdot (3 \sqrt{b^{2} \cdot (21 a b)})$

Step 2

Pull terms out from under the radical.

$2 \sqrt{15 a b} \cdot (3 (b \sqrt{21 a b}))$

Step 3

Multiply $2 \sqrt{15 a b} (3 b \sqrt{21 a b})$ .

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Step 3.1

Multiply $3$ by $2$ .

$6 \sqrt{15 a b} (b \sqrt{21 a b})$

Step 3.2

Combine using the product rule for radicals.

$6 (b \sqrt{15 a b (21 a b)})$

Step 3.3

Multiply $21$ by $15$ .

$6 (b \sqrt{315 a b (a b)})$

Step 3.4

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

$6 (b \sqrt{315 (a^{1} a) b \cdot b})$

Step 3.5

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

$6 (b \sqrt{315 (a^{1} a^{1}) b \cdot b})$

Step 3.6

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

$6 (b \sqrt{315 a^{1 + 1} b \cdot b})$

Step 3.7

Add $1$ and $1$ .

$6 (b \sqrt{315 a^{2} b \cdot b})$

Step 3.8

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

$6 (b \sqrt{315 a^{2} (b^{1} b)})$

Step 3.9

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

$6 (b \sqrt{315 a^{2} (b^{1} b^{1})})$

Step 3.10

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

$6 (b \sqrt{315 a^{2} b^{1 + 1}})$

Step 3.11

Add $1$ and $1$ .

$6 (b \sqrt{315 a^{2} b^{2}})$

Step 4

Rewrite $315 a^{2} b^{2}$ as ${(3 a b)}^{2} \cdot 35$ .

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Step 4.1

Factor $9$ out of $315$ .

$6 (b \sqrt{9 (35) a^{2} b^{2}})$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$6 (b \sqrt{3^{2} \cdot 35 a^{2} b^{2}})$

Step 4.3

Move $35$ .

$6 (b \sqrt{3^{2} a^{2} b^{2} \cdot 35})$

Step 4.4

Rewrite $3^{2} a^{2} b^{2}$ as ${(3 a b)}^{2}$ .

$6 (b \sqrt{{(3 a b)}^{2} \cdot 35})$

Step 5

Pull terms out from under the radical.

$6 (b (3 a b \sqrt{35}))$

Step 6

Multiply $b$ by $b$ by adding the exponents.

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Step 6.1

Move $b$ .

$6 (b \cdot b (3 a \sqrt{35}))$

Step 6.2

Multiply $b$ by $b$ .

$6 (b^{2} (3 a \sqrt{35}))$

Step 7

Rewrite using the commutative property of multiplication.

$6 (3 \sqrt{35} b^{2} a)$

Step 8

Multiply $3$ by $6$ .

$18 \sqrt{35} b^{2} a$