Question

Combine the radicals
sqrt 72 + sqrt 18

6sqrt7 - 4sqrt7




Multiply & express in simplest form
sqrt5 x sqrt20

1/3sqrt18 x sqrt16




Divide & express in simplest form
sqrt80 / sqrt5

sqrt150 / sqrt3



Rationalize the denominator
5
/
2-sqrt3


6
/
sqrt7+2



3
/
sqrt6

2+sqrt3
/
4-sqrt3

Answer 1

I will do the first one and the last one, you do the rest.
sqrt 72 + sqrt 18
=
sqrt (18*4) + sqrt 18
=
2 sqrt 18 + 1 sqrt 18
=
3 sqrt (3*3*2)
=
9 sqrt 2
-----------------------------
(2+sqrt 3) (4+sqrt3)
/
(4-sqrt 3) (4+sqrt3)
=
(8 +6sqrt 3 + 3 )
/
(16-3)
=
(11 +6 sqrt 3)
/
13

Answer 2

is there a way that the 1/3sqrt18 x sqrt16 problem can be solved

150 / 3

and
6
sqrt7 + 2


i'm having trouble with those.

Answer 3

If you mean (1/3)sqrt18 x sqrt16, that is (1/3)sqrt(9*2)* 4 = 4 sqrt 2

Surely you know what 150/3 is.