Pre-Algebra -Rationalizing

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A.)Simplify giving restrictions where necessary

1.) 3 square root 24

2.)4 square root 96  3.)square root y to the 7th power

4.) square root 18x to the 6th power y to the 11 th power

5.)the sa=quare root  of 15 x multiplied by the square root of 35xy

6.)3 square root 4a to the 8th power b to the 12th power

7.)4 square root 32x to the 9th power y to the 5th power z to the 12th power

8.)5 square root x to the 12th power y to the 4th power z to the 24th power

9.) 3 square root 9x squared multiplied by 3 square root 6x squared

10.)4 square root 8a squared b multiplied by 4 square root 4a^3rd power b to the 3rd power

11.)5 square root 8x to the 7th power ysquared multiplied by 5 square root 12x to the 4th power y to the 4th power

12.)9 square root x to the 6th power

 

b.)Rationalize the denominator.Assume all variables are positive.

 

1.)2 divided by square root 2

2.)4 square root 3 divided by 8

3.) suare root 3 divided by y

4.) square root x to the 5th power divided by 2

5.)1 divided by  4  square root x to the 3rd power

6.) square root 1 divided 2x to the 3rd powery to the 5th power

7.)3 square root 2x divided by 25y to the 5th power

8.)12x squared y squared divided by the square root 3x squared y

9.)14 divided by 3 square root 7y squared

10.)7xy divided by 3 square root -27x to the third power y

11.)5 square root 32xy squared divided by x to the 3rd power y

12.)3 to the square root x to the 5th power y to the 2nd power z divided by 3 the square root 16x squared yz

 

13.)Find three pairs of integers (x,y) with x<y that satisfy the equality

square root x +square root y =square root 75

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