Algebra Examples

$\sqrt{21 r} (5 + \sqrt{7})$

Step 1

Apply the distributive property.

$\sqrt{21 r} \cdot 5 + \sqrt{21 r} \sqrt{7}$

Step 2

Move $5$ to the left of $\sqrt{21 r}$ .

$5 \cdot \sqrt{21 r} + \sqrt{21 r} \sqrt{7}$

Step 3

Multiply $\sqrt{21 r} \sqrt{7}$ .

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Step 3.1

Combine using the product rule for radicals.

$5 \cdot \sqrt{21 r} + \sqrt{21 r \cdot 7}$

Step 3.2

Multiply $7$ by $21$ .

$5 \cdot \sqrt{21 r} + \sqrt{147 r}$

$5 \cdot \sqrt{21 r} + \sqrt{147 r}$

Step 4

Simplify each term.

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Step 4.1

Rewrite $147 r$ as $7^{2} \cdot (3 r)$ .

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Step 4.1.1

Factor $49$ out of $147$ .

$5 \sqrt{21 r} + \sqrt{49 (3) r}$

Step 4.1.2

Rewrite $49$ as $7^{2}$ .

$5 \sqrt{21 r} + \sqrt{7^{2} \cdot 3 r}$

Step 4.1.3

Add parentheses.

$5 \sqrt{21 r} + \sqrt{7^{2} \cdot (3 r)}$

$5 \sqrt{21 r} + \sqrt{7^{2} \cdot (3 r)}$

Step 4.2

Pull terms out from under the radical.

$5 \sqrt{21 r} + 7 \sqrt{3 r}$

$5 \sqrt{21 r} + 7 \sqrt{3 r}$

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