Solve sqrt[5]{64}-sqrt{98}+sqrt{162}

$$\sqrt[ 5 ] { 64 } - \sqrt { 98 } + \sqrt { 162 }$$

Evaluate

$$2\sqrt{2}+2^{\frac{6}{5}}\approx 5.125823835$$

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}.

$$\sqrt[5]{64}-7\sqrt{2}+\sqrt{162}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$\sqrt[5]{64}-7\sqrt{2}+9\sqrt{2}$$

Combine -7\sqrt{2} and 9\sqrt{2} to get 2\sqrt{2}.

$$\sqrt[5]{64}+2\sqrt{2}$$