Solve sqrt{12}(sqrt{3}-sqrt{8}

$$\sqrt { 12 } ( \sqrt { 3 } - \sqrt { 8 }$$

Evaluate

$$6-4\sqrt{6}\approx -3.797958971$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{3}\left(\sqrt{3}-\sqrt{8}\right)$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

$$2\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{2}$$

The square of \sqrt{3} is 3.

$$2\times 3-4\sqrt{3}\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$6-4\sqrt{3}\sqrt{2}$$

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

$$6-4\sqrt{6}$$