Solve 20sqrt{24}+1/2-4sqrt{8}

$$20 \sqrt { 24 } + \frac { 1 } { 2 } - 4 \sqrt { 8 }$$

Evaluate

$$40\sqrt{6}+\frac{1}{2}-8\sqrt{2}\approx 87.165881212$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$20\times 2\sqrt{6}+\frac{1}{2}-4\sqrt{8}$$

Multiply 20 and 2 to get 40.

$$40\sqrt{6}+\frac{1}{2}-4\sqrt{8}$$

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}.

$$40\sqrt{6}+\frac{1}{2}-4\times 2\sqrt{2}$$

Multiply -4 and 2 to get -8.

$$40\sqrt{6}+\frac{1}{2}-8\sqrt{2}$$

Factor

$$\frac{80 \sqrt{6} + 1 - 16 \sqrt{2}}{2} = 87.16588121234236$$