Solve (2-sqrt{3})(3-sqrt{12})

$$( 2 - \sqrt { 3 } ) ( 3 - \sqrt { 12 } )$$

Evaluate

$$12-7\sqrt{3}\approx -0.124355653$$

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}.

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

Apply the distributive property by multiplying each term of 2-\sqrt{3} by each term of 3-2\sqrt{3}.

$$6-4\sqrt{3}-3\sqrt{3}+2\left(\sqrt{3}\right)^{2}$$

Combine -4\sqrt{3} and -3\sqrt{3} to get -7\sqrt{3}.

$$6-7\sqrt{3}+2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$6-7\sqrt{3}+2\times 3$$

Multiply 2 and 3 to get 6.

$$6-7\sqrt{3}+6$$

Add 6 and 6 to get 12.

$$12-7\sqrt{3}$$