Solve 40sqrt{6}*frac{sqrt{6}+sqrt{2}}{4}

$$40 \sqrt { 6 } \times \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$$

Evaluate

$$20\sqrt{3}+60\approx 94.641016151$$

Solution Steps

Cancel out 4, the greatest common factor in 40 and 4.

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

Use the distributive property to multiply 10 by \sqrt{6}+\sqrt{2}.

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

Use the distributive property to multiply 10\sqrt{6}+10\sqrt{2} by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Multiply 10 and 6 to get 60.

$$60+10\sqrt{2}\sqrt{6}$$

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}.

$$60+10\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$60+10\times 2\sqrt{3}$$

Multiply 10 and 2 to get 20.

$$60+20\sqrt{3}$$