Precalculus Examples

$\sqrt{5 x} \cdot \sqrt{121 x}$

Step 1

Rewrite $121$ as $11^{2}$ .

$\sqrt{5 x} \cdot \sqrt{11^{2} x}$

Step 2

Pull terms out from under the radical.

$\sqrt{5 x} \cdot (11 \sqrt{x})$

Step 3

Rewrite using the commutative property of multiplication.

$11 \sqrt{5 x} \sqrt{x}$

Step 4

Multiply $11 \sqrt{5 x} \sqrt{x}$ .

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Step 4.1

Combine using the product rule for radicals.

$11 \sqrt{x (5 x)}$

Step 4.2

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

$11 \sqrt{5 (x^{1} x)}$

Step 4.3

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

$11 \sqrt{5 (x^{1} x^{1})}$

Step 4.4

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

$11 \sqrt{5 x^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$11 \sqrt{5 x^{2}}$

Step 5

Reorder $5$ and $x^{2}$ .

$11 \sqrt{x^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$11 x \sqrt{5}$