Quant basics - Arithmetic doubt

Question

In the lecture video "Exponents and Factorials - Practice" in Ques 6 -

(√5x-5)^2 is equal to 5x+25-10√5x. I do not understand how are we getting -10√5x (as part of the ans), should not (√5x-5)^2 be equal to 5x+25.

agarwal95 · Answer

Hi Jayesh,

Use the formula (a-b)^2= a^2-2*a*b+b^2 to expand (√5x-5)^2

On using the formula, 
= (√5x)^2-2*√5x*5+(5)^2
= 5x-10√5x+25

Posted from my mobile device

BrushMyQuant · Answer

Hi  jayjitesh1 
Am not from Crack Verbal But I can take a shot at this.

(\sqrt{5x}-5)^2  is of the form  (a-b)^2 
And we know that  (a-b)^2  =  a^2  - 2ab +  b^2 
So,  (\sqrt{5x}-5)^2  =  (\sqrt{5x})^2  - 2*  \sqrt{5x}  * 5 +  5^2 
= 5x -  10\sqrt{5x}  + 25

Hope it helps!

preeti95 · Answer

The formula for expansion is stated as below:

(a − b)^2 = a^2 − 2ab + b^2

In your example,

(√5x-5)^2 = (√5x)^2 - (2*√5x*5) + (5)^2 = 5x - 10√5x + 25

Do drop a kudos if this helps!!

CrackverbalGMAT · Answer

Hello jayjitesh1, 
If you face a difficulty in dealing with such expressions involving normal variables and roots, please assume the root to be equal to some variable; for example, you could have assumed √5x = k, isn’t it?

Had you done that, the expression given would have become (k-5)^2 which would have been simpler for you to expand. So, what would be (k-5)^2? It would be k^2 + 5^2 – 2*5*k, isn’t it?
You need to make problem solving easy for yourself by playing smart and not always try to play by the usual rules of the game.

And please memorise all the Algebraic identities, because going by the stem of your question, it seems like you are really not sure of which identity to use. (a-b)^2 is NOT equal to a^2 + b^2, isn’t it? Think about it.

Hope that helps!

Quant basics - Arithmetic doubt

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards