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

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

Evaluate

$$2\left(\sqrt{3}y+1\right)$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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}.

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

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

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

Differentiate w.r.t. y

$$2 \sqrt{3} = 3.464101615$$