Solve (4+2sqrt{6})(2+5sqrt{6})

$$( 4 + 2 \sqrt { 6 } ) ( 2 + 5 \sqrt { 6 } )$$

Evaluate

$$4\left(6\sqrt{6}+17\right)\approx 126.787753827$$

Solution Steps

Apply the distributive property by multiplying each term of 4+2\sqrt{6} by each term of 2+5\sqrt{6}.

$$8+20\sqrt{6}+4\sqrt{6}+10\left(\sqrt{6}\right)^{2}$$

Combine 20\sqrt{6} and 4\sqrt{6} to get 24\sqrt{6}.

$$8+24\sqrt{6}+10\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$8+24\sqrt{6}+10\times 6$$

Multiply 10 and 6 to get 60.

$$8+24\sqrt{6}+60$$

Add 8 and 60 to get 68.

$$68+24\sqrt{6}$$

Factor

$$4 {(6 \sqrt{6} + 17)} = 126.787753827$$