Solve left(1+3sqrt{2}right)-4-sqrt{50}

$$\left( 1+3 \sqrt{ 2 } \right) -4- \sqrt{ 50 }$$

Evaluate

$$-2\sqrt{2}-3\approx -5.828427125$$

Solution Steps

Subtract 4 from 1 to get -3.

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

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}.

$$-3+3\sqrt{2}-5\sqrt{2}$$

Combine 3\sqrt{2} and -5\sqrt{2} to get -2\sqrt{2}.

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