Square Roots

Square Root of Upto 5 digit Numbers
NOTE : We have to remember square of numbers from 1 to 31.This method is only applicable for perfect square of a number.

STEP 1: Make two pairs.

  • FIRST PAIR : Last two numbers
  • LAST PAIR : The remaining numbers.

Suppose a number is np, where n and p both are positive integers.

STEP 2: First we have to focus on last pair that is other remaining numbers.

  • To find square of a number which is less than and nearest to the last pair.
  • Calculate the square root of the square which gives the LHS answer. A2 < n < B 2 where A,B are postive integers. So n = A.

STEP 3: To get the unit’s place digit.

For example the given number ends with 4.Now we know that 22 and 82 are 4 and 64 respectively whose unit’s place is 4.From here we find that our RHS answer is either 2 or 8.

STEP 4:Combining together LHS and RHS answer then we get A2 or A8. Now we have to choose answer will be A2 or A8.

  • A2 < A5 < A8 ----[1]
  • Squaring 1,we get A22 < A52 < A82
  • Comparing the given number with A5.If A5 is greater than the given number then A2 will be the required answer. and If A5 is less than the given number then A8 will be the required answer

Now,we can easily find the answer.

NOTE : Here we take A5,because we can easily calculate the square of A5 and output of square of A5 whose unit's place is mirror image of unit’s place digit of the other numbers.
Examples

Example 1: Find square root of 121

STEP 1: 1 21

STEP 2: 12 < n < 2 2,So n=1 [LHS ANSWER]

STEP 3: The given number ends with 1.Now we know that 12 and 92 are 1 and 81 respectively whose unit’s place is 1.From here we find that our RHS answer is either 1 or 9.

STEP 4:Combining together LHS and RHS answer then we get 11 or 19. Now we have to choose answer will be 11 or 19.

  • 11 < 15 < 19 ----[1]
  • Squaring 1,we get 112 < 152 < 192
  • 112 < 225 < 192

So,225 is greater than 121.Hence 11 is the required answer.

Example 2: Find square root of 784

STEP 1: 7 84

STEP 2: 22 < n < 3 2,So n=2 [LHS ANSWER]

STEP 3: The given number ends with 4.Now we know that 22 and 82 are 1 and 81 respectively whose unit’s place is 4.From here we find that our RHS answer is either 2 or 8.

STEP 4:Combining together LHS and RHS answer then we get 22 or 28. Now we have to choose answer will be 22 or 28.

  • 22 < 25 < 29 ----[1]
  • Squaring 1,we get 222 < 25 2 < 282
  • 112 < 225 < 192

So,625 is less than 784.Hence 28 is the required answer.

Example 3: Find square root of 4489

STEP 1: 44 89

STEP 2: 62 < n < 7 2,So n=6 [LHS ANSWER]

STEP 3: The given number ends with 9. Now we know that 32 and 72 are 9 and 49 respectively whose unit’s place is 9.From here we find that our RHS answer is either 3 or 7.

STEP 4:Combining together LHS and RHS answer then we get 63 or 67. Now we have to choose answer will be 63 or 67.

  • 63 < 65 < 67 ----[1]
  • Squaring 1,we get 632 < 65 2 < 672
  • 112 < 4225 < 192

So,4225 is less than 4489.Hence 67 is the required answer.