# Aptitude - Square Root and Cube Root - Discussion

### Discussion :: Square Root and Cube Root - General Questions (Q.No.6)

6.

If a = 0.1039, then the value of 4a2 - 4a + 1 + 3a is:

 [A]. 0.1039 [B]. 0.2078 [C]. 1.1039 [D]. 2.1039

Explanation:

4a2 - 4a + 1 + 3a = (1)2 + (2a)2 - 2 x 1 x 2a + 3a

= (1 - 2a)2 + 3a

= (1 - 2a) + 3a

= (1 + a)

= (1 + 0.1039)

= 1.1039

 Bujji said: (Oct 9, 2010) How we get the formula. I can't understand, give me the clarification about it.

 Sundar said: (Oct 9, 2010) Formula: a2 + b2 - 2ab = (a - b)2

 Sarath said: (Oct 15, 2010) But I get (a-1/2) using (-b + -sqrt (b2 - 4ac) /2a).

 Mitz said: (Dec 10, 2010) In this case ans. Can also proceed with (2a - 1)^2 ??? Plz clarify !!

 Krishna said: (Dec 14, 2010) Sorry you are wrong 4*a*a - 4*a + 1 can be written as 4*a*a - 2*a -2*a +1 Taking 2*a common 2*a(2*a-1) -(2*a - 1) Hence (2*a-1)(2*a-1) but it is given as (1-2*a)(1-2*a) is completely wrong how can he get that ???? If im wrong please explain me ???

 Nikhil said: (Dec 28, 2010) The formula => a2 + b2 - 2ab = (a - b)2 can be a2 + b2 - 2ab = (b - a)2 as well. so we can get it as (2a - 1) +3a . Then the answer will be different.

 Dhildas said: (Feb 8, 2011) FOMULA (a-b) 2 is ok. But how square has gone from (1-2a) 2 and it written as (1-2a) +3a.

 Mariappan said: (Mar 1, 2011) Square root(a*a)=a similarly square root{(1-2a)*(1-2a)}=1-2a but my doubts is that why can't be (2a-1) Can any one help with this problem ?

 Tanvi said: (Mar 2, 2011) Yes, Mariapan, I agree with you. Why it's not (2a-1)?

 Rahul said: (Mar 3, 2011) +*- = - Then how it bcmz (1-2a)+3a = 1+a ? Anyone can tell?

 Pushpa said: (Mar 30, 2011) While I am solving getting (2a-1) or we can write (1-2a) also but why answer differs I mean according to options we should change ?

 Soumya said: (Apr 22, 2011) Krishna nice explanation.

 Rakesh. said: (May 15, 2011) I do agree with krishan, however 2a-1 is not equal to 1-2a because the value may be the same however, is it postive or negitive value, so can anyone explain on this?

 Bhargav said: (May 19, 2011) 4a2 - 4a + 1 (2a)2 - 2(2a)(1) + (1)2 (2a - 1)2 so, 2a - 1 + 3a Why 1 - 2a is here ???

 Sayani said: (Jun 4, 2011) I agree with those who has a doubt as why it won't be (2a-1)^2. should we change our ans according to the options available???

 Mannoj Kumar said: (Jun 12, 2011) I agree with sayani. We need to see the options also.

 Sid said: (Jun 24, 2011) Who goes for the answer anyone solving this would go for the formula asq - 2ab + bsq which will give (2a - 1)sq. I don't think (1-2a)sq can be the way out.

 Joginder said: (Aug 3, 2011) I have the same doubt, why cant it be (2a-1)2.

 Mithun said: (Aug 28, 2011) sqrt(4a2-4a+1)=2a-1 or 1-2a?

 Sudarsan said: (Sep 8, 2011) Your ans is right. But according to KRISHNA ,the sqrt of (2a-1)^2 is +(2a-1) and -(2a-1).so if we choose -(2a-1) then we get -(2a-1)+3a=-2a+1+3a =a+1 =.1039+1=1.1039 (ans) So, this is the technique to SATISFY the option, that has given in the question.

 Ravi said: (Sep 20, 2011) In the question why he has not taken as 2a-1^2 ?

 Anoop said: (Oct 17, 2011) Ravi because 2a<1, in our formula we have condition of a>b hope getting me correct me if I'm wrong.

 Sam said: (Jan 5, 2012) Anoop's ans shd be the right one....Thanks Anoop..

 C.M.Rafeek . Moothedam said: (Feb 9, 2012) I got answer 5a-1 ( 5*0.1039 ) - 1 ie -0.4805 How can 2a-1 and 1-2a be equal ?

 Prince said: (Aug 27, 2012) Please explain me these step =(1 - 2a)^2 + 3a = (1 - 2a) + 3a

 Kavitha said: (Oct 13, 2012) Please clarify why you are using (1-2a)^2. Why not (2a-1)^2.

 Manju said: (Jan 28, 2013) After solving we got (2a-1)^2 but according to answer we have to take like this: (2a-1)^2 = [-1(1-2a)]^2 (take -1 common from (2a-1)) = (-1)^2(1-2a)^2 (here -1*-1=1) = 1(1-2a)^2 = (1-2a)^2.

 Krishna said: (Jun 11, 2013) In a-b formula a

 Abhirup said: (Sep 13, 2013) Sq root of 4 is (+ or -) 2. Because when we do (+ or - 2)^2 in both cases its +4. Similarly +(1 - 2a)^2 is true and as well as -(1 - 2a)^2 i.e. (2a-1)^2 is also true. How ever the answer in two cases are different. So there must be an other answer except option C.

 Arpit said: (Sep 28, 2013) 4 = 2^2 and also 4=(-2)^2. So sqrt 4 = 2, -2. So sqrt 4a^2 -4a +1 = +(2a-1),-(2a-1). So we have choose any one of these such it satisfies the options available. +(2a-1) + 3a = 5a-1 = -1.5195 such option is not available. -(2a-1) + 3a = a+1 = 1.1039 this one is option C.

 Latha said: (Jan 7, 2014) a2-2ab+b2 = 4a2-4a+1. (a-b)2 it is in the form. Where a=(2a), b=1. So, (1-2a)2. 4a2-4a+1^2 = 1-2a^2. 1-2a+3a = a+1. 0.1039+1 = 1.1039.

 Souji said: (Jan 18, 2014) @Latha I have a doubt in your explanation. You said a=2a, b=1. While substitute you did(1-2a). But according to your explanation it is wrong. Actually it comes(2a-1).

 Rathi said: (Jan 20, 2014) @Souji. (1-2a)2 = (2a-1)2 = 4a2+1-4a. So no problem.

 Abhilash said: (Jan 31, 2014) According to the solution we have to follow! that is called reasoning!

 Iegarry@Gmail.Com said: (Aug 16, 2014) Let me explain this. When you solve the the equation under the square root, you can have either (2a - 1) or (1 - 2a). According to the question a = 0.1039. Hence, 2a-1 = 2* 0.1039 -1 which would be negative. You cannot have a negative number inside the square root though. Hence we have 1 - 2a.

 Nas said: (Aug 25, 2014) Guys let me explain this things. Everyone discuss here is (a-b)^2. Actually (a-b)^2= (b-a)^2. For example (5-2)^2=(2-5)^2. Cause square of a negative no is positive. But you guys know what's wrong in here. The wrong is square root of a no is either positive or negative. In solution taking square root come with +(1-2a) and -(1-2a) so while considering these two we get two answer. Both of them will satisfy the condition. Hope you guys are get it. Here solution consider only one possibilities of answer.

 Abul said: (Sep 14, 2014) Can anyone explain how (1-2a) instead of (2a-1) ?

 Saniya said: (Nov 21, 2014) The options are correct and even the answer is correct. By adopting the formula {a+b} = a^2+2ab+b^2.

 Lokesh Ravella said: (Nov 29, 2014) 4*a*a - 4*a + 1 can be written as 4*a*a - 2*a -2*a +1. Taking 2*a common 2*a(2*a-1)-(2*a - 1). Hence (2*a-1)(2*a-1). 4*a*a - 4*a + 1 can also be written as 1 + 4*a*a-4*a can be written as 1 + 4*a*a-2*a-2*a. 1 - 2*a + 4*a*a - 2*a. Taking 1 as common in first two and 2*a in last two then 1(1 - 2*a)-2*a(1 - 2*a). Hence (1 - 2*a)(1 - 2*a). So Both Are Correct. So we have to choose any one of these such it satisfies the options available.

 Shivam said: (Jan 24, 2015) Not getting how can we take decision at exam time.

 Barjinder Singh said: (Mar 30, 2015) Is there any other method to solve it?

 Sujith said: (May 19, 2015) We can use both (2a-1), (1-2a). Its just based on options they given.

 Shubham Bansal said: (Jul 21, 2015) Ok here we could check options but think if in any test both the answers are given then with which we have to go with.

 Ashit Patel said: (Aug 14, 2015) 2a-1=1-2a?

 Vishal said: (Sep 11, 2015) Since the value of a has been given in the question hence 2a-1 can't be square root since then the square root will be negative and options given as answers are positive. Hope you guys got it.

 Siddharth said: (Sep 17, 2015) Both (1-2a)^2 and (2a-1)^2 are correct we need to see from the options which answer is available.

 Phani said: (Nov 14, 2015) Why should we take (1-2a) and the given is 4a^2 -4a+1 we can also take 2a-1.

 Gupta said: (Nov 30, 2015) How is it 1-2a? It should be 2a-1.

 Renga said: (May 11, 2016) 2a - 1 + 3a = 5a - 1. = 5(0.1039) - 1 = -0.4805. Can you please explain, what is (1 - 2a)?

 Zareena said: (May 17, 2016) (1 - 2a)2 is wrong because if you expand it give 4a^2 + 4a + 1 which is not matching with the question. So, - 0.4805 is the right answer.

 Bhavuk Singh said: (Jun 11, 2016) Given , a = 0.1039 2a - 1= 2(0.1039) - 1 = - .7922. The square root of a negative number is not a real number. Hence, we use (1 - 2a).

 Jaju said: (Jun 25, 2016) Hi @Bhavuk Singh. How told you to take the square root of - .7922? Actually, when you take the square root of (2a-1) ^2 it will give you two result either 2a-1 else 1-2a. You can choose any of the two and yes, two results are possible here. Keeping in mind options given you have to select any one of twos. I think this is clear now?

 Harshit said: (Jun 29, 2016) Given that a = 0.1039; a<<1; this implies a^2<<<1 and hence it can be ignored int the expression. So, the value should be approximately equal to 1 - a = 0.8961. The exact value is 0.9393 is also nearly equal to it. But the option does not contain any matching value. So why should not we consider this question ambiguous?

 Rahul said: (Sep 4, 2016) I do not understand the explanation. Please clarify me.

 Divi said: (Sep 17, 2016) 4a^2 - 4a + 1 = (2a - 1)^2 Then square and root cancelld. 2a - 1 + 3a = 5a - 1. 5(0.1039) - 1 = 0.5195 - 1 = 0.4805 is this correct? I it is wrong, anyone explain me.

 Sandeep said: (Oct 28, 2016) @DIVI. Answer will be in -ve if you subtracting 0.5195 - 1.

 G Anirudh said: (Aug 22, 2017) Let me help you guys. Here the given question can have 2 different answers as; (1-2a)^2 = 4a^2-4a+1= (2a-1)^2. Hence for questions like these, try to verify with both the answers and select the given option. here answers are -0.4805 and 1.1039. so since all options are +ve we select the +ve ans i.e. 1.1039.

 Amitabha Das said: (Sep 6, 2017) It can also be (2a-1)^2.

 Maurya said: (Sep 10, 2017) Since all the options are positive we have to choose (1-2a).

 Shrikant T. said: (Dec 18, 2017) Here you have given the formula (x-y)^2. If we take the value of x = 2a and value of b = 1 then, (x-y)^2 = x^2 -2xy + y^2. i.e 4a^2 - 4a + 1. But here you have taken (1-2a)^2, which yields the completely different equation. Please correct and clarify.

 Sintu Kumar said: (Mar 1, 2018) @Krishna. But, my factor is (2a-1)(2a-1). Than 2a-1+3a, =5a-1, =5*0.1039-1. =0.5195-1=-0.4805.

 Surya said: (Mar 19, 2018) Why not 2a-1? How can 1-2a?

 Varsha Jadhav said: (Aug 14, 2018) @All. We can take positive or negative square root that is (2a-1) or -(2a-1) => (1-2a) but according to the given option we need a positive value if we consider the value (2a-1) then the answer will be negative. => (2a-1)+3a. => 5a-1, =>5*0.1039-1, =>0.5195-1, =>-0.4855. but if we put the value (1-2a) then the calculation will be; =>(1-2a)+3a. =>1+a, =>1+0.1039, =>1.1039.

 Dinesh Choudhury said: (Jul 29, 2019) 2a<1 so use (1-2a)^2. But (2a-1)^2 is a imaginary number.

 Chinnapa Reddy said: (Feb 22, 2020) I have one doubt about the solution to the problem why should we take 1-2*a only, there is another chance to take equation as 2*a-1 please tell me a solution.

 Khushi said: (Apr 20, 2020) Why w (1-2a) ^2, whekat ey not (2a-1) ^2? Please tell me.

 Siri said: (Aug 28, 2020) I am not understanding this whole solution, can someone explain to me in an easy manner?

 Mukesh Chauhan said: (Sep 29, 2020) Two answers are possible here. One is: 2a-1 and 1-2a because the square of both numbers are the same. Anyone, please clear this.

 Uyog said: (May 9, 2021) Guys..this will make you understand, Its 4a^2 * 4a+1... i.e a * 2ab+b^2.where a=2a...(4a^2) and b=1... So, we got formula of (a-b)^2..removing root..i.e (a-b). We get, (2a-1)+3. (2 * 0.1039- 1) + 3(0.1039). (0.2078-1) + 0.3117. 0.7922 + 0.31 17. 1.1039.

 Pallavi said: (Sep 27, 2021) Any anyone explain this clearly.