Question

how to get square roots of numbers having no perfect square

Answer 1

There are a number of ways to calculate square roots without a calculator. Here is guess and divide method.
Step–1: Estimate/find a perfect square root as close as possible to your number. Step–2: Divide your number by the square root. Step–3: Calculate the average of the result of step 2 and the root. Step–4: Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.
Calculate the square root of 10 (√ 10) to 4 decimal places.
1.    Find the perfect square number closer to 10. 32 = 9 and 42 = 16, so take 3. 2.    Divide 10 by 3. 10÷3 = 3.33 (you can round off the answer) 3.    Average 3.33 and 3. (3.33 + 3)÷2 = 3.1667
Repeat step 2: 10÷3.1667 = 3.1579 Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)÷2 = 3.1623
Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001
If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.