Exercise 35 Page 266

To simplify the given expression, we will use the FOIL method. Recall that the acronym F OI L stands for First, Outer, Inner, and Last. (6sqrt(5)+2)(4sqrt(2)+sqrt(3)) ⇕ ( 6sqrt(5))( 4sqrt(2)) + ( 6sqrt(5))( sqrt(3)) + (2)(4sqrt(2)) + ( 2)( sqrt(3)) Let's use perfect squares to simplify our radicals to see if we can create like terms.

(6sqrt(5))(4sqrt(2))+ (6sqrt(5))(sqrt(3)) + (2)(4sqrt(2)) +(2)(sqrt(3))

CommutativePropMult

Commutative Property of Multiplication

6 * 4 * sqrt(5) * sqrt(2)+ (6sqrt(5))(sqrt(3)) + (2)(4sqrt(2)) +(2)(sqrt(3))

ProdSqrt

sqrt(a)*sqrt(b)=sqrt(a* b)

6 * 4 * sqrt(5 * 2)+ 6 * sqrt(5 * 3) + (2)(4sqrt(2)) +(2)(sqrt(3))

Multiply

Multiply

24sqrt(10)+ 6sqrt(15) + 8sqrt(2) +2sqrt(3)

Radicals can only be added or subtracted when the index and the value inside are exactly the same. Therefore, we cannot simplify our expression any further.