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

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: a^{2} + b^{2} - 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<b is the condition so 1-2a is considered a=1 b=2a then 1-2a<0. 1<2a if a=1 then 1<2a. |

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} = 4a^{2}+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. |

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