Algebra Examples

$\sqrt{5} (\sqrt{15 x} + 3)$

Step 1

Apply the distributive property.

$\sqrt{5} \sqrt{15 x} + \sqrt{5} \cdot 3$

Step 2

Multiply $\sqrt{5} \sqrt{15 x}$ .

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{5 (15 x)} + \sqrt{5} \cdot 3$

Step 2.2

Multiply $5$ by $15$ .

$\sqrt{75 x} + \sqrt{5} \cdot 3$

$\sqrt{75 x} + \sqrt{5} \cdot 3$

Step 3

Move $3$ to the left of $\sqrt{5}$ .

$\sqrt{75 x} + 3 \cdot \sqrt{5}$

Step 4

Simplify each term.

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Step 4.1

Rewrite $75 x$ as $5^{2} \cdot (3 x)$ .

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Step 4.1.1

Factor $25$ out of $75$ .

$\sqrt{25 (3) x} + 3 \cdot \sqrt{5}$

Step 4.1.2

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

$\sqrt{5^{2} \cdot 3 x} + 3 \cdot \sqrt{5}$

Step 4.1.3

Add parentheses.

$\sqrt{5^{2} \cdot (3 x)} + 3 \cdot \sqrt{5}$

$\sqrt{5^{2} \cdot (3 x)} + 3 \cdot \sqrt{5}$

Step 4.2

Pull terms out from under the radical.

$5 \sqrt{3 x} + 3 \sqrt{5}$

$5 \sqrt{3 x} + 3 \sqrt{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$