Solve sqrt{56}div2sqrt{7}

$$\sqrt { 56 } \div 2 \sqrt { 7 }$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

Solution Steps

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{2\sqrt{14}}{2}\sqrt{7}$$

Cancel out 2 and 2.

$$\sqrt{14}\sqrt{7}$$

Factor 14=7\times 2. Rewrite the square root of the product \sqrt{7\times 2} as the product of square roots \sqrt{7}\sqrt{2}.

$$\sqrt{7}\sqrt{2}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$7\sqrt{2}$$