Solve (7-sqrt{6})*(3-sqrt{6})

$$( 7 - \sqrt { 6 } ) \cdot ( 3 - \sqrt { 6 } )$$

Evaluate

$$27-10\sqrt{6}\approx 2.505102572$$

Solution Steps

Apply the distributive property by multiplying each term of 7-\sqrt{6} by each term of 3-\sqrt{6}.

$$21-7\sqrt{6}-3\sqrt{6}+\left(\sqrt{6}\right)^{2}$$

Combine -7\sqrt{6} and -3\sqrt{6} to get -10\sqrt{6}.

$$21-10\sqrt{6}+\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$21-10\sqrt{6}+6$$

Add 21 and 6 to get 27.

$$27-10\sqrt{6}$$