Solve sqrt{98}-5sqrt{72}+sqrt{50}

$$\sqrt { 98 } - 5 \sqrt { 72 } + \sqrt { 50 }$$

Evaluate

$$-18\sqrt{2}\approx -25.455844123$$

Solution Steps

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}.

$$7\sqrt{2}-5\sqrt{72}+\sqrt{50}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$7\sqrt{2}-5\times 6\sqrt{2}+\sqrt{50}$$

Multiply -5 and 6 to get -30.

$$7\sqrt{2}-30\sqrt{2}+\sqrt{50}$$

Combine 7\sqrt{2} and -30\sqrt{2} to get -23\sqrt{2}.

$$-23\sqrt{2}+\sqrt{50}$$

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}.

$$-23\sqrt{2}+5\sqrt{2}$$

Combine -23\sqrt{2} and 5\sqrt{2} to get -18\sqrt{2}.

$$-18\sqrt{2}$$