Pre-Algebra Examples

$(\sqrt{125} + 1) (\sqrt{12 - 1})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 1.1.1

Factor $25$ out of $125$ .

$(\sqrt{25 (5)} + 1) \sqrt{12 - 1}$

Step 1.1.2

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

$(\sqrt{5^{2} \cdot 5} + 1) \sqrt{12 - 1}$

$(\sqrt{5^{2} \cdot 5} + 1) \sqrt{12 - 1}$

Step 1.2

Pull terms out from under the radical.

$(5 \sqrt{5} + 1) \sqrt{12 - 1}$

$(5 \sqrt{5} + 1) \sqrt{12 - 1}$

Step 2

Simplify by multiplying through.

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Step 2.1

Subtract $1$ from $12$ .

$(5 \sqrt{5} + 1) \sqrt{11}$

Step 2.2

Apply the distributive property.

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

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

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

$5 \sqrt{11 \cdot 5} + 1 \sqrt{11}$

Step 3.2

Multiply $11$ by $5$ .

$5 \sqrt{55} + 1 \sqrt{11}$

$5 \sqrt{55} + 1 \sqrt{11}$

Step 4

Multiply $\sqrt{11}$ by $1$ .

$5 \sqrt{55} + \sqrt{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{55} + \sqrt{11}$

Decimal Form:

$40.39761722 \dots$

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