Solve 3sqrt{2}(sqrt{10}-sqrt{3})

$$3 \sqrt { 2 } ( \sqrt { 10 } - \sqrt { 3 } )$$

Evaluate

$$6\sqrt{5}-3\sqrt{6}\approx 6.067938637$$

Solution Steps

Use the distributive property to multiply 3\sqrt{2} by \sqrt{10}-\sqrt{3}.

$$3\sqrt{2}\sqrt{10}-3\sqrt{3}\sqrt{2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$3\sqrt{2}\sqrt{2}\sqrt{5}-3\sqrt{3}\sqrt{2}$$

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

$$3\times 2\sqrt{5}-3\sqrt{3}\sqrt{2}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{5}-3\sqrt{3}\sqrt{2}$$

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

$$6\sqrt{5}-3\sqrt{6}$$