Question

find the square root of the following 1.4 161

Answer 1

Given:

A number 1.4161

To find:

Find the square root of the following 1.4161

Solution:

From given, we have,

A number 1.4161

we use the Hero's method to find the square root.

Step 1:

Divide the number (1.4161) by 2 to get the first guess for the square root.

Guess = 1.4161/2 = 0.70805.

Step 2:

Divide 1.4161 by the previous result.  

d = 1.4161/0.70805 = 2.

Average the value of d with that of step 1:  

(2 + 0.70805)/2 = 1.354025

Step 3:

Divide 1.4161 by the previous result.  

d = 1.4161/1.354025 = 1.0458447961.

Average the value of d with that of step 2:  

(1.0458447961 + 1.354025)/2 = 1.1999348981  

Step 4:

Divide 1.4161 by the previous result.  

d = 1.4161/1.1999348981 = 1.1801473582.

Average the value of d with that of step 3:  

(1.1801473582 + 1.1999348981)/2 = 1.1900411281  

Step 5:

Divide 1.4161 by the previous result.  

d = 1.4161/1.1900411281 = 1.1899588733.

Average the value of d with that of step 4:  

(1.1899588733 + 1.1900411281)/2 = 1.1900000007

Therefore, the square root of 1.4161 is 1.19

Answer 2

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