Solve 1/23sqrt{128}

$$\frac{ 1 }{ 2 } 3 \sqrt{ 128 }$$

Evaluate

$$12\sqrt{2}\approx 16.970562748$$

Solution Steps

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{3}{2}\sqrt{128}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{3}{2}\times 8\sqrt{2}$$

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

$$\frac{3\times 8}{2}\sqrt{2}$$

Multiply 3 and 8 to get 24.

$$\frac{24}{2}\sqrt{2}$$

Divide 24 by 2 to get 12.

$$12\sqrt{2}$$