Question

1. Estimate the square root of the following numbers upto one decimal place :
(i) 150
(ii) 390
(iii) 765
(iv) 40
(v) 920
(vi) 956​

Answer 1

Answer:

iii) the square root of 765 upto one decimal place is 27.6

Answer 2

Given : 150

To Find : Estimate the square root of the following numbers upto one decimal place

Solution:

 150

144 <  150 < 169

12² < 150 < 13²

Divide 150 by 12    ( we can divide by 13 also shown at end  )

150/12 = 12.5

Take average of 12 and 12.5

=  12.25

Divide 150 by 12.25

= 12.24

Hence Square root lies between 12.24 and 12.25

So upto one decimal = 12.2

if we took 13 instead of 12

Divide 150 by 13 =  11.54

Take mean of 13 and 11.54 =  12.27

Divide 150 by 12.27 = 12.22

Hence Square root of 150 lies between 12.22 and 12.27

Hence upto one decimal = 12.2

or use

f(x)  = √x  

f(150) = √150

f(x  +  Δx) = √(144 +6)

x = 144  Δx = 6

f'(x) = 1/2√x

f(x +  Δx)  = f(x)  + f'(x) Δx

=> √150  = √144  +  (1/2√144)(6)

=> √150  =12 +  0.25

=> √150  = 12.25

Similarly calculate for others

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