Solve sqrt{98}+sqrt{50}-sqrt{8}-sqrt{72}=

$$\sqrt{ 98 } + \sqrt{ 50 } - \sqrt{ 8 } - \sqrt{ 72 } =$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

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}.

$$7\sqrt{2}+\sqrt{50}-\sqrt{8}-\sqrt{72}$$

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}.

$$7\sqrt{2}+5\sqrt{2}-\sqrt{8}-\sqrt{72}$$

Combine 7\sqrt{2} and 5\sqrt{2} to get 12\sqrt{2}.

$$12\sqrt{2}-\sqrt{8}-\sqrt{72}$$

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}.

$$12\sqrt{2}-2\sqrt{2}-\sqrt{72}$$

Combine 12\sqrt{2} and -2\sqrt{2} to get 10\sqrt{2}.

$$10\sqrt{2}-\sqrt{72}$$

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}.

$$10\sqrt{2}-6\sqrt{2}$$

Combine 10\sqrt{2} and -6\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}$$