Solve 3sqrt{50}+2sqrt{8}-7sqrt{98}

$$3 \sqrt{ 50 } +2 \sqrt{ 8 } -7 \sqrt{ 98 }$$

Evaluate

$$-30\sqrt{2}\approx -42.426406871$$

Solution Steps

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}.

$$3\times 5\sqrt{2}+2\sqrt{8}-7\sqrt{98}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{2}+2\sqrt{8}-7\sqrt{98}$$

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}.

$$15\sqrt{2}+2\times 2\sqrt{2}-7\sqrt{98}$$

Multiply 2 and 2 to get 4.

$$15\sqrt{2}+4\sqrt{2}-7\sqrt{98}$$

Combine 15\sqrt{2} and 4\sqrt{2} to get 19\sqrt{2}.

$$19\sqrt{2}-7\sqrt{98}$$

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}.

$$19\sqrt{2}-7\times 7\sqrt{2}$$

Multiply -7 and 7 to get -49.

$$19\sqrt{2}-49\sqrt{2}$$

Combine 19\sqrt{2} and -49\sqrt{2} to get -30\sqrt{2}.

$$-30\sqrt{2}$$