Question

What square root best approximates the point on the graph?

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oooo1
N15
128
153

Answer 1

Using binomial expansion,

√

a

2

+

b

=

a

(

1

+

b

a

2

)

1

2

=

a

(

1

+

1

2

b

a

2

)

, nearly.

Here, choose a = 66 and b = 44.

Now,

√

4400

=

√

66

2

+

44

=

√

66

2

+

44

=

66

(

1

+

44

66

2

)

1

2

66

(

1

+

1

2

(

44

66

2

)

)

=

66

(

1

+

1

198

)

=

66

+

1

3

=

66.33

, nearly.

Note that the error is of order 66(1/198)^2=O(.002), nearly.

Step-by-step explanation: