Algebra Examples

$3 \sqrt{5 a \cdot 8 \sqrt{35 a^{2}}}$

Step 1

Multiply $8$ by $5$ .

$3 \sqrt{40 a \sqrt{35 a^{2}}}$

Step 2

Reorder $35$ and $a^{2}$ .

$3 \sqrt{40 a \sqrt{a^{2} \cdot 35}}$

Step 3

Pull terms out from under the radical.

$3 \sqrt{40 a \cdot a \sqrt{35}}$

Step 4

Combine exponents.

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Step 4.1

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

$3 \sqrt{40 (a^{1} a) \sqrt{35}}$

Step 4.2

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

$3 \sqrt{40 (a^{1} a^{1}) \sqrt{35}}$

Step 4.3

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

$3 \sqrt{40 a^{1 + 1} \sqrt{35}}$

Step 4.4

Add $1$ and $1$ .

$3 \sqrt{40 a^{2} \sqrt{35}}$

Step 5

Rewrite $40 a^{2} \sqrt{35}$ as ${(2 a)}^{2} \cdot (10 \sqrt{35})$ .

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Step 5.1

Factor $4$ out of $40$ .

$3 \sqrt{4 (10) a^{2} \sqrt{35}}$

Step 5.2

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

$3 \sqrt{2^{2} \cdot 10 a^{2} \sqrt{35}}$

Step 5.3

Move $10$ .

$3 \sqrt{2^{2} a^{2} \cdot 10 \sqrt{35}}$

Step 5.4

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

$3 \sqrt{{(2 a)}^{2} \cdot 10 \sqrt{35}}$

Step 5.5

Add parentheses.

$3 \sqrt{{(2 a)}^{2} \cdot (10 \sqrt{35})}$

Step 6

Pull terms out from under the radical.

$3 (2 a \sqrt{10 \sqrt{35}})$

Step 7

Multiply $2$ by $3$ .

$6 a \sqrt{10 \sqrt{35}}$