Solve 4sqrt{14}*1/2sqrt{7}

$$4 \sqrt{ 14 } \times \frac{ 1 }{ 2 } \sqrt{ 7 }$$

Evaluate

$$14\sqrt{2}\approx 19.798989873$$

Solution Steps

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}.

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

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

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

Multiply 4 and 7 to get 28.

$$28\times \frac{1}{2}\sqrt{2}$$

Multiply 28 and \frac{1}{2} to get \frac{28}{2}.

$$\frac{28}{2}\sqrt{2}$$

Divide 28 by 2 to get 14.

$$14\sqrt{2}$$