Solve sqrt{2}left(21+3sqrt{14}right)

$$\sqrt{ 2 } \left( 21+3 \sqrt{ 14 } \right)$$

Evaluate

$$6\sqrt{7}+21\sqrt{2}\approx 45.572992676$$

Solution Steps

Use the distributive property to multiply \sqrt{2} by 21+3\sqrt{14}.

$$21\sqrt{2}+3\sqrt{2}\sqrt{14}$$

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}.

$$21\sqrt{2}+3\sqrt{2}\sqrt{2}\sqrt{7}$$

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

$$21\sqrt{2}+3\times 2\sqrt{7}$$

Multiply 3 and 2 to get 6.

$$21\sqrt{2}+6\sqrt{7}$$

Factor

$$3 \sqrt{2} \sqrt{7} {(\sqrt{2} + \sqrt{7})} = 45.572992676$$