Question

Express the ratio of the area of the larger circle to the area of the smaller circle in simplest radical form. Larger circle: radius of 2 + √3 and smaller circle's radius: 2-√3.

Answer 1

is this a repost?
what was unclear on explainations in prev post?

Answer 2

Why is it 7 + 4√3?

Answer 3

I tried pi (2)^2 + √3^2

Answer 4

oh you forgot the middle term
(2+sqrt3)^2 = 4 + 2sqrt3 +2sqrt3 + 3

Answer 5

(a+b)^2 does Not equal (a^2 +b^2)

Answer 6

middle term? what? D:

Answer 7

FOIL ?

(2+sqrt3)(2+sqrt3) = 4+4sqrt3 +3

Answer 8

ohhh.

Answer 9

thank you!

Answer 10

:)

Answer 11

Okay so I have now: \[\pi \times 7 + 4\sqrt{3} \div \pi \times 7-4\sqrt{3} \times \pi \times 7+4\sqrt{3} \div \pi \times 7+4\sqrt{3}\]

Answer 12

yes except the pi cancels out...pi/pi = 1 so you can get rid of it

Answer 13

ohh..

Answer 14

Is that the same for 7/7?

Answer 15

no because its not a multiplicative constant...or its part of the addition so it can't cancel
it helps to put parenthesis around them, (7+4sqrt3) is like 1 term so only if (7+4sqrt3) is on bottom can it cancel
sorry if that was confusing

Answer 16

Okay so:

= \[(7 + 4\sqrt{3})(7 + 4\sqrt{3}) \div (7 - 4\sqrt{3})(7 + 4\sqrt{3})\]
= \[49 + 28\sqrt{3} + 28\sqrt{3} + 16\sqrt{9} \div 49 + 28\sqrt{3} - 28\sqrt{3} - 16\sqrt{9}\]
= \[121\sqrt{15} \div \]

Answer 17

\[33\sqrt{15}\]

Answer 18

The answer is supposed to be: 97 + 56√3

Answer 19

correct until last line...where did 121 come from?

Answer 20

also the numbers inside the radicals doNOt change when adding

Answer 21

oh i see what you did
... 2sqrt3 + 3sqrt2 does NOT equal 5sqrt5

keep the terms with radicals separate
you can only combine sqrt2 with other sqrt2 's

Answer 22

Top:
16sqrt9 = 16*3 = 48
28sqrt3 + 28sqrt3 = 56sqrt3
49 + 48 = 97
--> 97 + 56sqrt3

Bottom:
49 - 48 = 1
28sqrt3 - 28sqrt3 = 0
--> 1

Answer 23

ohhhh. Thank you!