Solve 3sqrt{18}-77sqrt{2}+2sqrt{50}

$$3 \sqrt { 18 } - 77 \sqrt { 2 } + 2 \sqrt { 50 }$$

Evaluate

$$-58\sqrt{2}\approx -82.024386618$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$3\times 3\sqrt{2}-77\sqrt{2}+2\sqrt{50}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}-77\sqrt{2}+2\sqrt{50}$$

Combine 9\sqrt{2} and -77\sqrt{2} to get -68\sqrt{2}.

$$-68\sqrt{2}+2\sqrt{50}$$

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}.

$$-68\sqrt{2}+2\times 5\sqrt{2}$$

Multiply 2 and 5 to get 10.

$$-68\sqrt{2}+10\sqrt{2}$$

Combine -68\sqrt{2} and 10\sqrt{2} to get -58\sqrt{2}.

$$-58\sqrt{2}$$