Here we are sharing some useful shortcut tricks for finding square,cube,square root and cube root which will be helpful in competitive exams.
Square-Shortcut Tricks
Method1:Apply
Examples:
Memorize this.
Method1:
Example1:
Step1: Divide digits into group of three from right to left 21 952
Step2: Last digit of rightmost group is 2.That means number ends with 8
Step3: Now consider leftmost group 21.Cube of 2=8 and cube of 3=27 ,since
21 is between them we must use smaller one,2. Thus final answer is 28
Example2 :
Step1: Divide digits into group of three from right to left 32 768
Step2: Last digit of rightmost group is 2.That means number ends with 8
Step3: Now consider leftmost group 32. Cube of 3=27 and cube of 4=64,since
32 is between them we must use smaller one,3. Thus final answer is 32.
Method2:Cube root by prime factorisation.
Examples:
Method2:Square of a number ending with 5
Suppose X5 is the number.
Suppose X5 is the number.
Examples:
Method3:Squres of numbers from 51-59
Add 25 to unit digit and square unit digit and concatenate two results
Examples:
Method4:square if you know square of previous number
Method3:Squres of numbers from 51-59
Add 25 to unit digit and square unit digit and concatenate two results
Examples:
Method4:square if you know square of previous number
Examples:
Method5:Square of a number if you know square of any other number.
Let X and Y be two numbers. You know the square of X then you can deduce square of Y.
Example:
Choose a nearby number whose square is known to you.Suppose we choose 110 whose square is 12100
Examples:
Method5:Square of a number if you know square of any other number.
Let X and Y be two numbers. You know the square of X then you can deduce square of Y.
Example:
Choose a nearby number whose square is known to you.Suppose we choose 110 whose square is 12100
Examples:
Cubes-Shortcut
Apply the formula
Examples:
Examples:
Square roots shortcuts (applicable only for perfect squares)
Method1:
Example1:Square root of 2704
Step1:Seperate number into group of two from right to left ie 27 04.
Step2:What number can be squared and less than 27=5, with remainder 2
Step3:Bringdown the second group of digits next to remainder to get 204
Step4:Double first part of answer to get 5*2=10
Step5:Find a number X so that 10 X * X= 204, we get X=2
Thus final answer=52
Example2:Square root of 9604
Step1:Seperate number into group of two from right to left ie 96 04.
Step2:What number can be squared and less than 96=9, with remainder 15
Step3:Bringdown the second group of digits next to remainder to get 1504
Step4:Double first part of answer to get 9*2=18
Step5:Find a number X so that 18 X * X= 1504, we get X=8
Thus final answer=98
Method2:Square root by prime factorisation.
Examples:
Example1:Square root of 2704
Step1:Seperate number into group of two from right to left ie 27 04.
Step2:What number can be squared and less than 27=5, with remainder 2
Step3:Bringdown the second group of digits next to remainder to get 204
Step4:Double first part of answer to get 5*2=10
Step5:Find a number X so that 10 X * X= 204, we get X=2
Thus final answer=52
Example2:Square root of 9604
Step1:Seperate number into group of two from right to left ie 96 04.
Step2:What number can be squared and less than 96=9, with remainder 15
Step3:Bringdown the second group of digits next to remainder to get 1504
Step4:Double first part of answer to get 9*2=18
Step5:Find a number X so that 18 X * X= 1504, we get X=8
Thus final answer=98
Method2:Square root by prime factorisation.
Examples:
Properties of a perfect square
- No perfect square ends with 2,3,7,8
- No perfect square ends with an odd number of zeros.
- The perfect square consisting of (n-1) or n digits will have n/2 digits in their root.
- The square of a number other than unity is either a multiple of 4 or exceeds a multiple of 4 by 1.
Cube root shortcuts(for perfect cubes only)
Memorize this.
Method1:
Example1:
Step1: Divide digits into group of three from right to left 21 952
Step2: Last digit of rightmost group is 2.That means number ends with 8
Step3: Now consider leftmost group 21.Cube of 2=8 and cube of 3=27 ,since
21 is between them we must use smaller one,2. Thus final answer is 28
Example2 :
Step1: Divide digits into group of three from right to left 32 768
Step2: Last digit of rightmost group is 2.That means number ends with 8
Step3: Now consider leftmost group 32. Cube of 3=27 and cube of 4=64,since
32 is between them we must use smaller one,3. Thus final answer is 32.
Method2:Cube root by prime factorisation.