Pre-Algebra Examples

$\sqrt{72} + \frac{1}{4} \sqrt{98}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.1.1

Factor $36$ out of $72$ .

$\sqrt{36 (2)} + \frac{1}{4} \cdot \sqrt{98}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2} + \frac{1}{4} \cdot \sqrt{98}$

Step 1.2

Pull terms out from under the radical.

$6 \sqrt{2} + \frac{1}{4} \cdot \sqrt{98}$

Step 1.3

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.3.1

Factor $49$ out of $98$ .

$6 \sqrt{2} + \frac{1}{4} \cdot \sqrt{49 (2)}$

Step 1.3.2

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

$6 \sqrt{2} + \frac{1}{4} \cdot \sqrt{7^{2} \cdot 2}$

Step 1.4

Pull terms out from under the radical.

$6 \sqrt{2} + \frac{1}{4} \cdot (7 \sqrt{2})$

Step 1.5

Multiply $\frac{1}{4} (7 \sqrt{2})$ .

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Step 1.5.1

Combine $7$ and $\frac{1}{4}$ .

$6 \sqrt{2} + \frac{7}{4} \sqrt{2}$

Step 1.5.2

Combine $\frac{7}{4}$ and $\sqrt{2}$ .

$6 \sqrt{2} + \frac{7 \sqrt{2}}{4}$

Step 2

To write $6 \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$6 \sqrt{2} \cdot \frac{4}{4} + \frac{7 \sqrt{2}}{4}$

Step 3

Combine fractions.

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Step 3.1

Combine $6 \sqrt{2}$ and $\frac{4}{4}$ .

$\frac{6 \sqrt{2} \cdot 4}{4} + \frac{7 \sqrt{2}}{4}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{6 \sqrt{2} \cdot 4 + 7 \sqrt{2}}{4}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $4$ by $6$ .

$\frac{24 \sqrt{2} + 7 \sqrt{2}}{4}$

Step 4.2

Add $24 \sqrt{2}$ and $7 \sqrt{2}$ .

$\frac{31 \sqrt{2}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{31 \sqrt{2}}{4}$

Decimal Form:

$10.96015510 \dots$