Solve sqrt{162}-10sqrt{128}

$$\sqrt { 162 } - 10 \sqrt { 128 }$$

Evaluate

$$-71\sqrt{2}\approx -100.409162928$$

Solution Steps

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$9\sqrt{2}-10\sqrt{128}$$

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}.

$$9\sqrt{2}-10\times 8\sqrt{2}$$

Multiply -10 and 8 to get -80.

$$9\sqrt{2}-80\sqrt{2}$$

Combine 9\sqrt{2} and -80\sqrt{2} to get -71\sqrt{2}.

$$-71\sqrt{2}$$