Solve sqrt{128}+2sqrt{98}-3sqrt{162}

$$\sqrt { 128 } + 2 \sqrt { 98 } - 3 \sqrt { 162 }$$

Evaluate

$$-5\sqrt{2}\approx -7.071067812$$

Solution Steps

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}.

$$8\sqrt{2}+2\sqrt{98}-3\sqrt{162}$$

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}.

$$8\sqrt{2}+2\times 7\sqrt{2}-3\sqrt{162}$$

Multiply 2 and 7 to get 14.

$$8\sqrt{2}+14\sqrt{2}-3\sqrt{162}$$

Combine 8\sqrt{2} and 14\sqrt{2} to get 22\sqrt{2}.

$$22\sqrt{2}-3\sqrt{162}$$

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}.

$$22\sqrt{2}-3\times 9\sqrt{2}$$

Multiply -3 and 9 to get -27.

$$22\sqrt{2}-27\sqrt{2}$$

Combine 22\sqrt{2} and -27\sqrt{2} to get -5\sqrt{2}.

$$-5\sqrt{2}$$