Question about square roots and sums

[noravoningersleben]

Hi all,

I have a general question that doesn't refer to any specific MGMAT problem. I hope this is the right forum to post this question (it seemed to be the most suitable forum out of all the different options) - if not, I apologize.

Here is my question:

If we have an expression such as sqrt (25)(30) + (8)(32), we can't "draw out" from underneath the square root 5 (because 25 is 5^2), 2 (because 8 is 2^3) and 4 (because 32 is 2^5) to get 40 sqrt 30+ (2)(2), right? Why not, though? Because we're dealing with a sum here? But (25)(30) and (8)(32) are products and so we should be allowed to simplify as above, right?

Sorry, I know this is kind of a strange question - but I'm trying to understand why we're not allowed to simplify as above. Thanks in advance for any help!

[shyamprasadrao]

sqrt ( a*a*c + a*a*b) = sqrt (a*a(c+b))
which becomes sqrt(a*a)* sqrt(c+b)

sqrt ( a*a*c + b*b*d) how can you simplify this into two terms multiplying each other.
i.e can this above equation be deduced to sqrt (X*Y) form. No hence we cannot do what you
had mentioned

If this is not clear please let me know

P.S. sqrt can be split on to terms, only if they are being multiplied or divided.

[RonPurewal]

Hi all,

I have a general question that doesn't refer to any specific MGMAT problem. I hope this is the right forum to post this question (it seemed to be the most suitable forum out of all the different options) - if not, I apologize.

Here is my question:

If we have an expression such as sqrt (25)(30) + (8)(32), we can't "draw out" from underneath the square root 5 (because 25 is 5^2), 2 (because 8 is 2^3) and 4 (because 32 is 2^5) to get 40 sqrt 30+ (2)(2), right? Why not, though? Because we're dealing with a sum here? But (25)(30) and (8)(32) are products and so we should be allowed to simplify as above, right?

Sorry, I know this is kind of a strange question - but I'm trying to understand why we're not allowed to simplify as above. Thanks in advance for any help!

the problem here actually doesn't have anything to do with a square root. it's a more basic problem of factoring/distributing.

namely:
you can't FACTOR SOMETHING OUT OF A SUM/DIFFERENCE unless it is IN EACH AND EVERY TERM OF THE SUM/DIFFERENCE.

think about why you can't factor a "3" out of (3x + 5y).
this is the same reason you can't perform the factorizations above.

[noravoningersleben]

gotcha, thanks to both of you!

[Ben Ku]

Glad your question was answered!