Solve 2sqrt{2}(5sqrt{2}+sqrt{6})

$$2 \sqrt { 2 } ( 5 \sqrt { 2 } + \sqrt { 6 } )$$

Evaluate

$$4\left(\sqrt{3}+5\right)\approx 26.92820323$$

Solution Steps

Use the distributive property to multiply 2\sqrt{2} by 5\sqrt{2}+\sqrt{6}.

$$10\left(\sqrt{2}\right)^{2}+2\sqrt{2}\sqrt{6}$$

The square of \sqrt{2} is 2.

$$10\times 2+2\sqrt{2}\sqrt{6}$$

Multiply 10 and 2 to get 20.

$$20+2\sqrt{2}\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$20+2\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$20+2\times 2\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$20+4\sqrt{3}$$