use bisection method to find the positive square root of 30 correct to 4 decimal places
Answers
Given : square root of 30
√30
To Find : the positive square root of 30 correct to 4 decimal places using bisection method
Solution:
x = √30
x² = 30
=> x² - 30 = 0
5² - 30 = - 5 < 0
6² - 30 = 6 > 0
Hence
Lies between 5 and 6
mean of 5 and 6 = 5.5
x = 5.5
=> 5.5² - 30 = 0.25 > 0
Hence lies between 5 and 5.5
as for 5 its < 0 and for 5.5 > 0
Now take Mean of 5 and 5.5 and repeat the this process
x x^2-30
5 -5 -ve
6 6 +ve
5.5 0.25 +ve
5.25 -2.4375 -ve
5.375 -1.109375 -ve
5.4375 -0.43359375 -ve
5.46875 -0.092773438 -ve
5.484375 0.078369141 +ve
5.4765625 -0.007263184 -ve
5.48046875 0.03553772 +ve
5.478515625 0.014133453 +ve
5.477539063 0.003434181 +ve
5.477050781 -0.00191474 -ve
5.477294922 0.000759661 +ve
5.477172852 -0.000577554 -ve
5.477233887 9.10498E-05 +ve
5.477203369 -0.000243253 -ve
5.477218628 -7.61019E-05
5.4772 is repeated 3 times
Hence positive square root of 30 correct to 4 decimal places = 5.4772
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