Question

Find the principal (positive) square root of 22. if necessary, round the answer to the nearest hundredth (two decimal places).

Answer 1

Step 1

Find the two perfect square numbers it lies between.

Solution:
4²= 16 and 5² = 25, so  lies between 4 and 5.

step 2

Divide 22 by 4. 22/4 = 5.5 (you can round off your answer)

step 3

Average 5.5 and 4. (5.5+4)/2 = 4.75

step 4

repeat step 2

Divide 22 by 4.75. 22/4.75 = 4.6316

step 5

repeat step 3

Average 4.75 and 4.6316. (4.75+4.6316)/2 = 4.6908

the answer is

4.69