Solve sqrt{128}-sqrt{98}+sqrt{75}

$$\sqrt { 128 } - \sqrt { 98 } + \sqrt { 75 }$$

Evaluate

$$\sqrt{2}+5\sqrt{3}\approx 10.0744676$$

Solution Steps

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}.

$$8\sqrt{2}-\sqrt{98}+\sqrt{75}$$

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}.

$$8\sqrt{2}-7\sqrt{2}+\sqrt{75}$$

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

$$\sqrt{2}+\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

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