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4 years ago

Help help! 50+ points plus Brainlist answer if work is shown!

Mathematics

1 answer:

3241004551 [841]4 years ago

6 0

Answer:

4 sqrt(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)

--------------------

Simplify

2 sqrt(36 *5)

--------------------

We know that sqrt(ab) = sqrt(a) sqrt(b)

2 sqrt(36)sqrt(5)

--------------------------

2 *6*sqrt(5)

-------------------

Simplify

2 * 2 sqrt(5)

---------------------

4 sqrt(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)

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