Squares and Square Roots Shortcuts for Bank Exam

Method for finding Square Roots:

By the Square of a number, it means the product of number by the number itself. if a² = b, we say that square root of b is a and we write here square of b = a².

Rules for Squares:

• A square of a natural number can not end with 2,3,7,8 and an odd number of zeros.
• The square of an odd number is odd that of an even number is even.
• Every square number is a multiple of 3 or exceeds a multiple of 3 by unity.
• Every square number is a multiple of 4 or exceeds a multiple of 4 by unity.
• If a square number ends in 9, the preceding digits is even.

Methods for Finding Square Roots:

In any competitive exam time is very important, when you are using short cuts in solving a problem then automatically you can solve more questions. Here I was explained how to find square root for a given number with example.

Example: Find the Square root of 4624 ?

Solution: For the above question the answer is 68

Explanation: Here you just remember 0 to 9 digits squares and its unit digits.

Square		unit digit
0	0	0
1	1	1
2	4	4
3	9	9
4	16	6
5	25	5
6	36	6
7	49	9
8	64	4
9	81	1

√ 4624 = ?
Step 1: Consider last two digits of a given number. In the above example the last digits are 24, in this two digits consider only UNIT digit. Here the Unit digit is 4, from the above table the unit digit 4 should comes to square of 2 and square 8.
Step 2: Now assume in the answer the unit digit should be either 2 or 8.
Step 3: Now consider the number rest of last two digits, in the above example the remaining part is 46
Step 4: Here we consider the exact square of the 46, it should be precede of the 46,
Actually the nearest square of 46 is 49 and 36. but 49 is exceed 46, so don't consider 49. just you consider 36 only, 36 is the square of 6
Step 5: Now the answer is nearest square number and unit digit. i.e.
 62 or 68
Now Here apply the multiplication short cut:
The exact number between 60 to 70 is 65. Here in the given question the approximate answer is near to 65. if you know the square of 65 you can find answer quickly.
the square of 65 is 4225.
65² =

Rest of unit digit x next digit	unit digit square
6x7	5x5
42	25

 
65² = 4225
In given question 4624 is greater than the 65 square, so the final answer  is 68.

Examples:

1. √1089
2. √841
3. √2116
4. √12544
5. √4489

Note: Dear aspirants practice is important for every one. especially you need more practice for competitive exams, for the above method looking is lengthy but once you start the practice for solving square roots it will take less than 15 seconds.

Short Cuts on Number System
Short cuts for Divisibility Rules
Finding Cube Root Short Cuts