Solve 60left(sqrt{6}-sqrt{2}right)*sqrt{3}

$$60 \left( \sqrt{ 6 } - \sqrt{ 2 } \right) \times \sqrt{ 3 }$$

Evaluate

$$180\sqrt{2}-60\sqrt{6}\approx 107.58905666$$

Solution Steps

Use the distributive property to multiply 60 by \sqrt{6}-\sqrt{2}.

$$\left(60\sqrt{6}-60\sqrt{2}\right)\sqrt{3}$$

Use the distributive property to multiply 60\sqrt{6}-60\sqrt{2} by \sqrt{3}.

$$60\sqrt{6}\sqrt{3}-60\sqrt{2}\sqrt{3}$$

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

$$60\sqrt{3}\sqrt{2}\sqrt{3}-60\sqrt{2}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$60\times 3\sqrt{2}-60\sqrt{2}\sqrt{3}$$

Multiply 60 and 3 to get 180.

$$180\sqrt{2}-60\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$180\sqrt{2}-60\sqrt{6}$$