Solve sqrt{72}+1/4sqrt{98}

$$\sqrt { 72 } + \frac { 1 } { 4 } \sqrt { 98 }$$

Evaluate

$$\frac{31\sqrt{2}}{4}\approx 10.960155108$$

Solution Steps

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}.

$$6\sqrt{2}+\frac{1}{4}\sqrt{98}$$

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}.

$$6\sqrt{2}+\frac{1}{4}\times 7\sqrt{2}$$

Multiply \frac{1}{4} and 7 to get \frac{7}{4}.

$$6\sqrt{2}+\frac{7}{4}\sqrt{2}$$

Combine 6\sqrt{2} and \frac{7}{4}\sqrt{2} to get \frac{31}{4}\sqrt{2}.

$$\frac{31}{4}\sqrt{2}$$