Question

How to take out squareroot ?

Answer 1

The square root of a number, n, written
$\sqrt{n}$ is the number that gives n when multiplied by itself.
For example, $\sqrt{100}=10$ because 10 $\times$ 10 = 100.
Examples
Here are the square roots of all the perfect squares from 1 to 100.
$\sqrt{1}=1$ since $1^2=1$
$\sqrt{4}=2$ since $2^2=4$
$\sqrt{9}=3$ since $3^2=9$
$\sqrt{16}=4$ since $4^2=16$
$\sqrt{25}=5$ since $5^2=25$
$\sqrt{36}=6$ since $6^2=36$
$\sqrt{49}=7$ since $7^2=49$
$\sqrt{64}=8$ since $8^2=64$
$\sqrt{81}=9$ since $9^2=81$
$\sqrt{100}=10$ since ${10}^2=100$
Finding square roots of of numbers that aren't perfect squares:
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 $\left(10\sqrt{10}\right)$ to 2 decimal places.
1. Find the two perfect square numbers it lies between.
Solution:
32 = 9 and 42 = 16, so lies between 3 and 4.
2. Divide 10 by 3. $\frac{10}{3}=3.33$ (you can round off your answer)
3. Average 3.33 and 3. $\frac{(3.33+3)}{2}=3.1667$
Repeat step 2: $\frac{10}{3.1667}=3.1579$
Repeat step 3: Average 3.1579 and $\mathrm{3.1667.}\frac{(3.1579+3.1667)}{2}=3.1623$
Try the answer $\to$ Is 3.1623 squared equal to 10? 3.1623 $\times$ 3.1623 = 10.0001
If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.