Solve sqrt{14}(sqrt{7}+sqrt{2})

$$\sqrt { 14 } ( \sqrt { 7 } + \sqrt { 2 } )$$

Evaluate

$$2\sqrt{7}+7\sqrt{2}\approx 15.190997559$$

Solution Steps

Use the distributive property to multiply \sqrt{14} by \sqrt{7}+\sqrt{2}.

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

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}.

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

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

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

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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