Solve 1-3/4sqrt{2}sqrt{2}

$$1- \frac{ 3 }{ 4 \sqrt{ 2 } } \sqrt{ 2 }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Rationalize the denominator of \frac{3}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$1-\frac{3\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}\sqrt{2}$$

The square of \sqrt{2} is 2.

$$1-\frac{3\sqrt{2}}{4\times 2}\sqrt{2}$$

Multiply 4 and 2 to get 8.

$$1-\frac{3\sqrt{2}}{8}\sqrt{2}$$

Express \frac{3\sqrt{2}}{8}\sqrt{2} as a single fraction.

$$1-\frac{3\sqrt{2}\sqrt{2}}{8}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$1-\frac{3\times 2}{8}$$

Multiply 3 and 2 to get 6.

$$1-\frac{6}{8}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$1-\frac{3}{4}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{4}-\frac{3}{4}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{4}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$