How to find a Square root of a number?
The first method is inter-related to this one. This method is applicable only for
perfect squares.
You have to follow Three simple steps.
1. Find the range
2. Check the Unit Digit.
3. Find the square of number ending with 5 in the particular range and fix the
number.
a) What is the square root of 484?
Step 1
We all know 202 = 400. Also we know 302 = 900.
So our number lies between 20 and 30.
Step 2
The unit digit is 4. So the unit digit of square root can be either 2 or 8. The
number can be either 22 or 28.
Step 3
Between 20 and 30, we can easily find the square of 25 using the first method.
252 = (2 x 3)25 = 625
484 is less than 25. So Answer is 22.
b) What is the square root of 9801?
Range – 90 to 100.
Square of 95 = (9 x 10) 25 = 9025.
Answer can be either 91 or 99. (Based on Unit Digit)
9025 is less than 9801. So 99 is the Answer.
What is the Square root of 112896?
Range – 300 to 350 (As it is a big number, we need to follow one more step)
Now we should reduce the range. Square of 33 is 1089. So 3302 will be 108900.
Square of 34 is 1156. So 3402 will be 115600. Our number is in between 330
and 240. As the unit digit is 6, there are two possibilities. It can be either 334 or
336.
Square of 335 = (33 x 34) 25 = (11 x 3 x 34) 25 = (374 x 3) 25= 112225.
As our number is more than the square of 335, the Answer is 336.
Note: This method may look tough and time consuming. But it is really a simple
one.
d) What is the Square root of 390625?
Range
Square of 600 – 360000. Square of 650 – (6 x 7)2500 = 422500. (By Method 1).
So it is in between 60 and 65.
As the unit digit is 5, the square root should also end with 5. The options we
have are 605, 615, 625, 635, and 645.
We can easily eliminate 605 and 645. (Based on Difference)
Note : These steps can be done by just seeing the number and mainly with out
using pen.
Square of 615 = (61 x 62)25 = (62 (60 + 1))25 = 378225
Square of 625 = (62 x 63)25 = (63 (60 + 2))25 = 390625
Practice Problems.
Find the Square Root of
1. 5776
2. 140625
3. 828100
