Pre-Algebra Examples

$\sqrt{11} (7 - \sqrt{20})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1.1

Factor $4$ out of $20$ .

$\sqrt{11} (7 - \sqrt{4 (5)})$

Step 1.1.2

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

$\sqrt{11} (7 - \sqrt{2^{2} \cdot 5})$

$\sqrt{11} (7 - \sqrt{2^{2} \cdot 5})$

Step 1.2

Pull terms out from under the radical.

$\sqrt{11} (7 - (2 \sqrt{5}))$

Step 1.3

Multiply $2$ by $- 1$ .

$\sqrt{11} (7 - 2 \sqrt{5})$

$\sqrt{11} (7 - 2 \sqrt{5})$

Step 2

Apply the distributive property.

$\sqrt{11} \cdot 7 + \sqrt{11} (- 2 \sqrt{5})$

Step 3

Move $7$ to the left of $\sqrt{11}$ .

$7 \cdot \sqrt{11} + \sqrt{11} (- 2 \sqrt{5})$

Step 4

Multiply $\sqrt{11} (- 2 \sqrt{5})$ .

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Step 4.1

Combine using the product rule for radicals.

$7 \cdot \sqrt{11} - 2 \sqrt{11 \cdot 5}$

Step 4.2

Multiply $11$ by $5$ .

$7 \cdot \sqrt{11} - 2 \sqrt{55}$

$7 \sqrt{11} - 2 \sqrt{55}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{11} - 2 \sqrt{55}$

Decimal Form:

$8.38397655 \dots$

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