Solve sqrt{98}+sqrt{128}-sqrt{188}

$$\sqrt { 98 } + \sqrt { 128 } - \sqrt { 188 }$$

Evaluate

$$15\sqrt{2}-2\sqrt{47}\approx 7.501894235$$

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}.

$$7\sqrt{2}+\sqrt{128}-\sqrt{188}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$7\sqrt{2}+8\sqrt{2}-\sqrt{188}$$

Combine 7\sqrt{2} and 8\sqrt{2} to get 15\sqrt{2}.

$$15\sqrt{2}-\sqrt{188}$$

Factor 188=2^{2}\times 47. Rewrite the square root of the product \sqrt{2^{2}\times 47} as the product of square roots \sqrt{2^{2}}\sqrt{47}. Take the square root of 2^{2}.

$$15\sqrt{2}-2\sqrt{47}$$