Problem Solving

sqrrt of (4sqrrt80 +4/9+4sqrrt5)

I don't remind answering your question, but I'm really confused by the way you have it written. is the the whole top portion divided by /9 or /9+sqrtXX)

Tommieboi918 wrote:sqrrt of (4sqrrt80 +4/9+4sqrrt5)

Answer choices would be helpful. Anyways i got sqr418/3 as answer.

first simplify all the terms inside the sqrt.

4sqrt80 = 16sqrt5

Therefore we would have 4/9 + 20sqrt5 => 4+180sqrt5/9

sqrt5 = 2.3

180*2.3 = 414

sqrt (418/9) => sqrt418/3

Let me know the if this the correct answer and if you need any explanations.

The 9 only divides the 4 in the formula ( I think)

I finish at this: 2 * sqrt ( 5sqrt(5) + 1/9 )
I don't think it can be merely solved

sorry for the misunderstanding and confusion...I dont really know how to post problems in sqrrt...so heres another shot at it ..hopes this clarifies some things..

(the whole problem is under the sqrrt):

sqrt: (4sqrt80 + (4 divided by [9+4sqrrt5])) =

a)[4sqrt5]/9
b) 2
c)[4sqrt5+2]/[3+2sqrt5]
d) 6
e) 36

btw this is solvable and the correct ans is d: 6...but it doesnt explain how to get there.... hopes this clarifies it. thanks

also only the 4 in the second half after the + is divided by 9+4sqrt5...the 4sqrt80 stands alone without division

Tommieboi918 wrote:sorry for the misunderstanding and confusion...I dont really know how to post problems in sqrrt...so heres another shot at it ..hopes this clarifies some things..

(the whole problem is under the sqrrt):

sqrt: (4sqrt80 + (4 divided by [9+4sqrrt5])) =

a)[4sqrt5]/9
b) 2
c)[4sqrt5+2]/[3+2sqrt5]
d) 6
e) 36

btw this is solvable and the correct ans is d: 6...but it doesnt explain how to get there.... hopes this clarifies it. thanks

Thanks for posting the answer choices.

Here is goes:

Firstly leave the Whole sqrt, we can take care of it later

Lets solve for the terms inside

4sqrt80 + [4 / (9+4sqrt5)]

=> [4sqrt80(9+4sqrt5) + 4] / (9+4sqrt5)

=> [16sqrt5(9+4sqrt5) + 4] / (9+4sqrt5)

=> [144sqrt5 + 324] / (9+4sqrt5)

=> [36 (4sqrt5 +9 ) ] / (9+4sqrt5)

Now we cancel the 4sqrt5 + 9 since it is in the denominator as well as numerator

=> 36

dont forget about the whole sqrt

=> sqrt36 => 6

Hence answer D.

Hope this helps. Let me know if you still have any doubts.

The process for answering this type of question is called "rationalizing a denominator." The strategy on this type of question is to look at the operation. If the operation in the denominator is addition you can expect the answer to either be rational or have subtraction as an operation. If the operation is subtraction you can expect the answer to be rational or have addition as an operation.

(4sqrt80 + (4 divided by [9+4sqrrt5]))

the sqrt of 80 = sqrt of 16 X sqrt of 5; sqrt of 16 = 4

(16sqrt5) + (4 / [9 +4sqrt5]))

Rationalize the denominator of the second term, using the difference of squares:

(16sqrt5 + (4 / [9+4sqrt5])([9-4sqrt5] / [9-4sqrt5]))

Distribute in the numerator and denominator of the second term.

(16sqrt5 + ([36 - 16sqrt5] / [81 - 16*5])

16*5 = 80, so the denominator in the second term = 81-80 = 1

(16 sqrt5 + [(36 - 16sqrt5) / 1]

The 1 is not necessary in the denominator.

16sqrt5 + 36 - 16sqrt5

16sqrt5 - 16sqrt5 = 0, so we are left with the sqrt of 36 which equals 6.

Thanks that rationalizing is certainly better..
Saves time..

I'm a little confused. When would using the rationalization strategy be a good idea?

hengirl03 wrote:I'm a little confused. When would using the rationalization strategy be a good idea?

Well that would depend upon the answer choices and question. But it is always a good strategy to rationalize when you see a sqrt or cube root in denominator.

Yeah I dont think GMAT expects you to rationalize, of course if you are stuck I guess you have no choice. I believe the cancellation is the trick to be used here if you wish to save some time..