Rationalizing the denominator! PLEASE PLEASE PLEASE help?!?!?

Question

These are multiple choice so it makes it that much easier. Please help me solve some? First right answer=Best Answer!

1.) √25/√2
√2/2
5√2/2
3√2/2

2.) √18/10
√5/5
2√5/5
3√5/5

3.) √a^2/√2a
√a/2
√a
√2a/2

4.) 4/√x-√y
4(√x+√y)
4(√x+√y)/x
4(√x+√y)/x-y

5.) 7√3/3- √2
√3(√3+√2)
√3(3+√2)
3(√3+√2)

6.) 7/5-√11
5+√11/3
5+√11/2
2+√11/5

Answer 1

1) 5√2/2
2) 3√5/5
3) √(2a)/2
4) 4(√x+√y)/(x-y)
5) √3(3+√2)
6) 5+√11/2

6) 7/(5-√11)
Like #4 use the conjugate 5+√11. Multiply the top and bottom by the conjugate and you get:
(35 + 7√11)/(25 - 11)=
(35 + 7√11)/(14) =
5+√11/2

Answer 2

1.) √25/√2 =
5√2/2


2.) √(18/10) =
3√5/5

3.) √a^2/√2a =
√2a/2

4.) 4/√x-√y =
4(√x+√y)/(x-y)

5.) 7√3/(3- √2) =
√3(3+√2)

6.) 7/(5-√11) =
(5+√11)/2

Answer 3

1.) 5√2/2



2.) 3√5/5

3.) √2a/2


4.) 4(√x+√y)/x-y

5.) √3(3+√2)


6.) 5+√11/2

Answer 4

with the aid of multiplying the the two the denominator and the numerator with the aid of four-?2 you're cancelling out a sq. root in view which you will get sixteen-4?2+4?2-2 interior the denominator. with the aid of multiplying with the aid of four+?2 you will not cancel out and nevertheless finally end up with a sq. root interior the denominator (sixteen+4?2+4?2+2 or 18+8?2) which does not rationalize. there's a acceptance for the alternative sign subject yet i overlook it now. wish it is right and that i helped haha :)

Answer 5

1) 5 / sq rt 2 = 5 sq rt 2 / 2

2) sq rt (9)(2) / 10 = 3 sq rt 2 / 10
If both are in sq rt then sq rt (9/5) = 3 /sq rt 5 =
3 sq rt 5 / 5

3) a / sq rt 2a= a sq rt 2a/ 2a = sq rt 2a / 2

4)Mult by conjugate
4 (sq rt x +sq rt y) / x - y

5) 7 sq rt 3(3 + sq rt 2) / 7 = sq rt 3(3 + sq rt 2)

6) 7(5 + sq rt 11)/14 = 5 + sq rt 11/2

Answer 6

1. 5√2/2
2.3√5/5
3.√2a/2
4.4(√x+√y)/x-y
5.√3(3+√2)
6.5+√11/2

Answer 7

1) 5/2 sqr(2)
2) 3/5 sqr(5)
3) sqr(2a)/2
4) 4 [ sqr(x) -sqr(y) ] / ( x -y )
5) not so clear
6) not so clear

Answer 8

1).sqrt(25)/sqrt(2)=5/sqrt(2)
5/sqrt(2)xsqrt(2/sqrt(2)
=5sqrt(2)/2 third option.
4. 4/[sqrt(x-sqrt(y)]x[]sqrt(x+sqrt(y)/[sqrt(x+sqrt(y)]
=4[]sqrt(x-sqrt(y)/(x-y)option 4. answer