Help with this math please?

Question

1: Rationalize these radical expressions:

sqrt 45/ sqrt 5

2: sqrt 35/ sqrt 7

3: sqrt 6x/7

4: sqrt 45x^2/ sqrt 9

5: sqrt 14x/18x

6: sqrt 75xy^7/12xy

7: sqrt 2x/9x

Answer 1

I'll do the first one, since the steps are all similar, you should be able to do the rest:

√45 / √5

You want to remove the radical from the denominator.  So multiply both sides of the fraction by √5, and this happens:

√(45) √(5) / [√(5) * √(5) ]

since 45 = 9 * 5:

√9 * √5 * √5 / 5

3 * 5 / 5

3

Answer 2

sqrt 45/ sqrt 5= sqrt(45*5)/5=(sqrt225)/5=15/5=3

2: sqrt 35/ sqrt 7=sqrt245/7=7sqrt5/7= sqrt5

3: sqrt (6x/7)=sqrt(42x)/7

4: sqrt 45x^2/ sqrt 9=3x sqrt5/3=x sqrt5

5: sqrt(14x/18x)= sqrt(7/9)= sqrt(7)/3

6: sqrt (75xy^7/12xy)=[5y^3 sqrt(3)]/2sqrt3=5y^3/2

7: sqrt (2x/9x)= (sqrt2)/3

Answer 3

√45/√9=√45/9 = √5

√35/√7=√35/7=√5

3cant do anything

√45√x^2/√9 = x√9√5/ √9 = x√5

√14x/18x = √ 7/√9 = √7/3

√75xy^7/√12xy = √25√3√x√y^6√y / √4√3√x√y

= 5y^3/2

√2x/√9x

√2/(3)