Question

Find the square root of the following(correct to 3 decimal places) 45.34

Answer 1

Given:

A number 45.34

To find:

Find the square root of the following(correct to 3 decimal places) 45.34

Solution:

From given, we have,

A number 45.34

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

Step 1:

Divide the number (45.34) by 2 to get the first guess for the square root.

Guess = 45.34/2 = 22.67.

Step 2:

Divide 45.34 by the previous result.

d = 45.34/22.67 = 2.

Average the value of d with that of step 1:

(2 + 22.67)/2 = 12.335  

Step 3:

Divide 45.34 by the previous result.

d = 45.34/12.335 = 3.6757194974.

Average the value of d with that of step 2:

(3.6757194974 + 12.335)/2 = 8.0053597487  

Step 4:

Divide 45.34 by the previous result.

d = 45.34/8.0053597487 = 5.6637054952.

Average the value of d with that of step 3:

(5.6637054952 + 8.0053597487)/2 = 6.834532622  

Step 5:

Divide 45.34 by the previous result.

d = 45.34/6.834532622 = 6.6339576541.

Average the value of d with that of step 4:

(6.6339576541 + 6.834532622)/2 = 6.734245138  

Step 6:

Divide 45.34 by the previous result.

d = 45.34/6.734245138 = 6.7327516404.

Average the value of d with that of step 5:

(6.7327516404 + 6.734245138)/2 = 6.7334983892  

Therefore, the square root of 45.34 is 6.733.

Answer 2

Answer:

45.37 by three decimal places