Algebra Examples

$3 - \sqrt{49 + 2 (3 + 4^{2}) \div \frac{1}{2}}$

Step 1

To write $49$ as a fraction with a common denominator, multiply by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$3 - \sqrt{\frac{49 (\frac{1}{2})}{\frac{1}{2}} + 2 (3 + 4^{2}) \div \frac{1}{2}}$

Step 2

Combine the numerators over the common denominator.

$3 - \sqrt{\frac{49 (\frac{1}{2}) + 2 (3 + 4^{2})}{\frac{1}{2}}}$

Step 3

Rewrite $\frac{49 (\frac{1}{2}) + 2 (3 + 4^{2})}{\frac{1}{2}}$ in a factored form.

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Step 3.1

Combine $49$ and $\frac{1}{2}$ .

$3 - \sqrt{\frac{\frac{49}{2} + 2 (3 + 4^{2})}{\frac{1}{2}}}$

Step 3.2

Raise $4$ to the power of $2$ .

$3 - \sqrt{\frac{\frac{49}{2} + 2 (3 + 16)}{\frac{1}{2}}}$

Step 3.3

Add $3$ and $16$ .

$3 - \sqrt{\frac{\frac{49}{2} + 2 \cdot 19}{\frac{1}{2}}}$

Step 3.4

Multiply $2$ by $19$ .

$3 - \sqrt{\frac{\frac{49}{2} + 38}{\frac{1}{2}}}$

Step 3.5

To write $38$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 - \sqrt{\frac{\frac{49}{2} + 38 \cdot \frac{2}{2}}{\frac{1}{2}}}$

Step 3.6

Combine $38$ and $\frac{2}{2}$ .

$3 - \sqrt{\frac{\frac{49}{2} + \frac{38 \cdot 2}{2}}{\frac{1}{2}}}$

Step 3.7

Combine the numerators over the common denominator.

$3 - \sqrt{\frac{\frac{49 + 38 \cdot 2}{2}}{\frac{1}{2}}}$

Step 3.8

Simplify the numerator.

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Step 3.8.1

Multiply $38$ by $2$ .

$3 - \sqrt{\frac{\frac{49 + 76}{2}}{\frac{1}{2}}}$

Step 3.8.2

Add $49$ and $76$ .

$3 - \sqrt{\frac{\frac{125}{2}}{\frac{1}{2}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$3 - \sqrt{\frac{125}{2} \cdot 2}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$3 - \sqrt{\frac{125}{2} \cdot 2}$

Step 5.2

Rewrite the expression.

$3 - \sqrt{125}$

Step 6

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

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Step 6.1

Factor $25$ out of $125$ .

$3 - \sqrt{25 (5)}$

Step 6.2

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

$3 - \sqrt{5^{2} \cdot 5}$

Step 7

Pull terms out from under the radical.

$3 - (5 \sqrt{5})$

Step 8

Multiply $5$ by $- 1$ .

$3 - 5 \sqrt{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$3 - 5 \sqrt{5}$

Decimal Form:

$- 8.18033988 \dots$