Basic Math Examples

$\sqrt{3 {fg}^{2}} \cdot \sqrt{3 fg}$

Step 1

Combine using the product rule for radicals.

$\sqrt{3 {fg}^{2} \cdot 3 fg}$

Step 2

Multiply $3$ by $3$ .

$\sqrt{9 {fg}^{2} fg}$

Step 3

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

$\sqrt{9 ({fg}^{1} {fg}^{2})}$

Step 4

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

$\sqrt{9 {fg}^{1 + 2}}$

Step 5

Add $1$ and $2$ .

$\sqrt{9 {fg}^{3}}$

Step 6

Rewrite $9 {fg}^{3}$ as ${(3 fg)}^{2} fg$ .

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Step 6.1

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

$\sqrt{3^{2} {fg}^{3}}$

Step 6.2

Factor out ${fg}^{2}$ .

$\sqrt{3^{2} ({fg}^{2} fg)}$

Step 6.3

Rewrite $3^{2} {fg}^{2}$ as ${(3 fg)}^{2}$ .

$\sqrt{{(3 fg)}^{2} fg}$

Step 7

Pull terms out from under the radical.

$3 fg \sqrt{fg}$

Step 8

Reorder factors in $3 fg \sqrt{fg}$ .

$3 \sqrt{fg} fg$