Solve 3/4sqrt{8}

$$\frac { 3 } { 4 } \sqrt { 8 }$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Express \frac{3}{4}\times 2 as a single fraction.

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

Multiply 3 and 2 to get 6.

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

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}\sqrt{2}$$