You are Here: Home >< Maths

# uh, binomial thing? easy? watch

1. ...with these values of a and b, use the result (1 + 2x)^0.5 ≈ (1 + ax)/(1 + bx), with x = -0.01, to obtain an approximation of root 2, in the form p/q.

---

i obtained a and b by expanding and equating the left hand side of the equation above. but now, how does letting x = -0.01 help me get to 2^0.5 ?
2. (1+2x)^.5

with x as -0.01
=(0.98)^.5

=(2*0.49)^.5

=0.49^.5(2)^.5

=(0.7)*(2)^.5

(2)^.5=(1 - 0.01a)/0.7(1 - 0.01b)

??? is this right im not too sure myself
3. 1-.02 = 49/50

√(49/50) = 7/ √50 = 7/ 5√2 multiplying by √2 = 7√2 /10

is the relation you may be looking for, recognize a similar question.

edit: with the binomial approximation does it ask for a certain degree of accuracy i.e. what power of x are you going up to?
4. (Original post by Infinity_Kev)
(1+2x)^.5

with x as -0.01
=(0.98)^.5

=(2*0.49)^.5

=0.49^.5(2)^.5

=(1/7)*(2)^.5

(2)^.5=(1 - 0.01a)/7(1 - 0.01b)

??? is this right im not too sure myself
i presume this line should be 0.7√2? i get the idea, thanks.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: August 30, 2005
Today on TSR

Uni realities

### University open days

• University of Lincoln
Mini Open Day at the Brayford Campus Undergraduate
Wed, 19 Dec '18
• University of East Anglia
Fri, 4 Jan '19
• Bournemouth University
Wed, 9 Jan '19
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams