Solve 8sqrt{8}-7sqrt{98}-6sqrt{50}

$$8 \sqrt { 8 } - 7 \sqrt { 98 } - 6 \sqrt { 50 }$$

Evaluate

$$-63\sqrt{2}\approx -89.09545443$$

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}.

$$8\times 2\sqrt{2}-7\sqrt{98}-6\sqrt{50}$$

Multiply 8 and 2 to get 16.

$$16\sqrt{2}-7\sqrt{98}-6\sqrt{50}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$16\sqrt{2}-7\times 7\sqrt{2}-6\sqrt{50}$$

Multiply -7 and 7 to get -49.

$$16\sqrt{2}-49\sqrt{2}-6\sqrt{50}$$

Combine 16\sqrt{2} and -49\sqrt{2} to get -33\sqrt{2}.

$$-33\sqrt{2}-6\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$-33\sqrt{2}-6\times 5\sqrt{2}$$

Multiply -6 and 5 to get -30.

$$-33\sqrt{2}-30\sqrt{2}$$

Combine -33\sqrt{2} and -30\sqrt{2} to get -63\sqrt{2}.

$$-63\sqrt{2}$$