Solve 1-sqrt{2*12/88+88}

$$1 - \sqrt { \frac { 2 \times 12 } { 88 + 88 } }$$

Evaluate

$$-\frac{\sqrt{66}}{22}+1\approx 0.630725527$$

Short Solution Steps

Multiply 2 and 12 to get 24.

$$1-\sqrt{\frac{24}{88+88}}$$

Add 88 and 88 to get 176.

$$1-\sqrt{\frac{24}{176}}$$

Reduce the fraction \frac{24}{176} to lowest terms by extracting and canceling out 8.

$$1-\sqrt{\frac{3}{22}}$$

Rewrite the square root of the division \sqrt{\frac{3}{22}} as the division of square roots \frac{\sqrt{3}}{\sqrt{22}}.

$$1-\frac{\sqrt{3}}{\sqrt{22}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{22}} by multiplying numerator and denominator by \sqrt{22}.

$$1-\frac{\sqrt{3}\sqrt{22}}{\left(\sqrt{22}\right)^{2}}$$

The square of \sqrt{22} is 22.

$$1-\frac{\sqrt{3}\sqrt{22}}{22}$$

To multiply \sqrt{3} and \sqrt{22}, multiply the numbers under the square root.

$$1-\frac{\sqrt{66}}{22}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{22}{22}.

$$\frac{22}{22}-\frac{\sqrt{66}}{22}$$

Since \frac{22}{22} and \frac{\sqrt{66}}{22} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-\sqrt{66}}{22}$$