Simplify each expression (10 POINTS!)

1. 5√6(√3 - 2√7)

2. (4√5 + √3)(2√2 - √7)

3. (√12 - √2)(√12 + √2)

4. (3√x + 2)^2

5. 8/(3 + √2)

5√6(1√3) + 5√6(2√7)

5(1)(√(6x3)) + 5(2)(√(6x7))

5√18 + 10√42

5(√(9x2)) + 10√42

5(3(√2)) + 10√42

15√2 + 10√42

can't simplify further.




(4√5 + √3)(2√2 - 1√7)

4√5(2√2) + 4√5(-1√7) + 1√3(2√2) + 1√3)(-1√7)

4(2)(√(5x2)) + 4(-1)(√(5x7)) + 1(2)(√(3x2)) + 1(-1)(√(3x7))

8√10 - 4√35 + 2√6 - 1√21

8√10 - 4√35 + 2√6 - √21

can't simplfiy further.





(√12 - √2)(√12 + √2)

√12(√12) + √12(√2) - √2(√12) - √2(√2)

√(12x12) + √(12x2) - √(12x2) - √(2x2)

√144 + √24 - √24 - √4

12 - 2

10





(3√x + 2)(3√x + 2)

(3√x + 2√1)(3√x + 2√1)

3√x(3√x) + 3√x(2√1) + 2√1(3√x) + 2√1(2√1)

3(3)(√(xtimesx)) + 3(2)(√(1timesx)) + (2)(3)√(1timesx)) + 2(2)(√(1times1)

9√x^2 + 6√x + 6√x + 4√1

9(x^(2/2)) + 12√x + 4(1)

9x^1 + 12√x + 4

9x + 12√x + 4

can't simplify further.






8 / (3 + √2)

rationalize the denominator by multiplying top and bottom by the denomiantors conjugate: (3 - √2)

8(3 - √2) / (3 +√2)(3 - √2)

[8(3) + 8√1(-1√2)] / [3(3) + 3(-√2) + √2(3) +√2(-1√2)]

[24 + 8(-1)(√(1x2)] / [9 - 3√2 + 3√2 - √(2x2)]

[24 - 8√2] / [9 - √4]

[24 - 8√2] / [9 - 2]

(24 - 8√2) / 7

can't simplify further.

1. 5√6(√3 - 2√7)

2. (4√5 + √3)(2√2 - √7)

3. (√12 - √2)(√12 + √2)

4. (3√x + 2)^2

5. 8/(3 + √2)
cW/ P;. 236727uk