**By Soo Jin Lee and Jaehong Shin**

__Day2__

Last time we learned the concept of perfect squares and squaring roots.(If you are not comforatbe with these notions yet, review the previous section by clicking here.)

Today we will find square roots of numbers that are not perfect squares without calculator.

There are four steps you need to do for this objects.

1.** Estimate**- first, get as close
as you can by finding two perfect square roots your number is
between.

2.** Divide**- divide your number
by one of those square roots.

3.** Average**- take the average of
the result of step 2 and the root.

4.Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.

**Example: Calculate the square root of 10
to 2 decimal places.**

**1**. Find the two
perfect square numbers it lies between.

Solution:

3^2 = 9 and 4^2 = 16, so lies between 3 and 4.

**2**. Divide 10
by 3.

10/3 = 3.33 (you can round off your answer)

**3.** Average 3.33
and 3.

(3.33 + 3)/2 = 3.1667

**Repeat step 2**:
10/2.1667 = 3.1579

**Repeat step 3: **Average
of 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the answer-----> Is 3.1623 squared equal to 10? 3.1623 * 3.1623 = 10.0001

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and step 3.

**Note : **There
are a number of ways to calculate square root without calculator.