Solve (8sqrt{2}-5)*(10sqrt{2}-6)

$$( 8 \sqrt { 2 } - 5 ) \times ( 10 \sqrt { 2 } - 6 )$$

Evaluate

$$190-98\sqrt{2}\approx 51.407070887$$

Solution Steps

Apply the distributive property by multiplying each term of 8\sqrt{2}-5 by each term of 10\sqrt{2}-6.

$$80\left(\sqrt{2}\right)^{2}-48\sqrt{2}-50\sqrt{2}+30$$

The square of \sqrt{2} is 2.

$$80\times 2-48\sqrt{2}-50\sqrt{2}+30$$

Multiply 80 and 2 to get 160.

$$160-48\sqrt{2}-50\sqrt{2}+30$$

Combine -48\sqrt{2} and -50\sqrt{2} to get -98\sqrt{2}.

$$160-98\sqrt{2}+30$$

Add 160 and 30 to get 190.

$$190-98\sqrt{2}$$

Factor

$$2 {(95 - 49 \sqrt{2})} = 51.407070887$$