Answer:
4 sqrt(5)
-----------------
5
83 +12 sqrt(35)
Step-by-step explanation:
1. 4 sqrt(6)
--------------------
sqrt(30)
Multiply the top and bottom by sqrt(30) to rationalize the denominator
4 sqrt(6) *sqrt(30)
--------------------
sqrt(30)*sqrt(30)
4 sqrt(180)
--------------------
30
Simplify
2 sqrt(36 *5)
--------------------
15
We know that sqrt(ab) = sqrt(a) sqrt(b)
2 sqrt(36)sqrt(5)
--------------------------
15
2 *6*sqrt(5)
-------------------
15
Simplify
2 * 2 sqrt(5)
---------------------
5
4 sqrt(5)
-----------------
5
2. (2 sqrt(5) + 3 sqrt(7))^2
(2 sqrt(5) + 3 sqrt(7)) (2 sqrt(5) + 3 sqrt(7))
FOIL
first 2sqrt(5)*2sqrt(5)=4*5=20
outer 2 sqrt(5) * 3 sqrt(7) = 6 sqrt(35)
inner 3 sqrt(7) *2 sqrt(5) = 6 sqrt(35)
last 3sqrt(7) 3sqrt(7) = 9*7 = 63
Add them together = 20 + 6 sqrt(35)+ 6 sqrt(35) +63 = 83 +12 sqrt(35)
