Solve (2+5sqrt{2})(4-3sqrt{2})

$$( 2 + 5 \sqrt { 2 } ) ( 4 - 3 \sqrt { 2 } )$$

Evaluate

$$14\sqrt{2}-22\approx -2.201010127$$

Solution Steps

Apply the distributive property by multiplying each term of 2+5\sqrt{2} by each term of 4-3\sqrt{2}.

$$8-6\sqrt{2}+20\sqrt{2}-15\left(\sqrt{2}\right)^{2}$$

Combine -6\sqrt{2} and 20\sqrt{2} to get 14\sqrt{2}.

$$8+14\sqrt{2}-15\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$8+14\sqrt{2}-15\times 2$$

Multiply -15 and 2 to get -30.

$$8+14\sqrt{2}-30$$

Subtract 30 from 8 to get -22.

$$-22+14\sqrt{2}$$

Factor

$$2 {(7 \sqrt{2} - 11)} = -2.201010127$$