Solve sqrt{7}(sqrt{14}-5sqrt{7})

$$\sqrt { 7 } ( \sqrt { 14 } - 5 \sqrt { 7 } )$$

Evaluate

$$7\left(\sqrt{2}-5\right)\approx -25.100505063$$

Solution Steps

Use the distributive property to multiply \sqrt{7} by \sqrt{14}-5\sqrt{7}.

$$\sqrt{7}\sqrt{14}-5\left(\sqrt{7}\right)^{2}$$

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}.

$$\sqrt{7}\sqrt{7}\sqrt{2}-5\left(\sqrt{7}\right)^{2}$$

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

$$7\sqrt{2}-5\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7\sqrt{2}-5\times 7$$

Multiply -5 and 7 to get -35.

$$7\sqrt{2}-35$$