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Squaring in Vedic Maths



In Vedic mathematics, two types of techniques are in use - specific technique and general technique. For example the technique of squaring numbers ending with 5 is aspecific technique, because it can square only numbers ending with 5. It can not be used to square any other number. On the other hand, technique of multiplication as given by criss cross system is a general technique. general technique has a wider scope.

Square of numbers ending with 5s

Example 1

Find the square of 45 (45)2

45 X 45 = 20 25

Technique:

Step 1: Multiply 5 with with 5 and write 25

Step 2: In 45 the number apart from 5 is 4.

the next number to 4 is 5. Multiply 4 with 5 and write 20.

The answer is 2025

Example 2

Find the square of 65 (65)2

65 X 65 = 42 25

Technique:

Step 1: Multiply 5 with with 5 and write 25

Step 2: In 65 the number apart from 5 is 6.

the next number to 6 is 7. Multiply 6 with 7 and write 42.

The answer is 2025



Exercise:

  1. (15)2

  2. (25)2

  3. (35)2

  4. (55)2

  5. (75)2

  6. (85)2

  7. (95)2

  8. (115)2

  9. (105)2

  10. (1005)2

  11. (205)2

  12. (305)2

Answers

1. 225 2. 625 3. 1225 4. 3025 5. 5625 6. 7225 7. 9025 8. 13225 9. 11025 10. 1100025 11. 41025 12. 91025

Squaring of numbers between 50 to 60 i.e., 51, 52, 53, 54, 55, 56, 57, 58, 59

Example 1 Find the square of 57 (57)2

57 X 57 = 3249

Technique:

There are two digits 5 and 7

Add 25 to 7 and write on the left side (32).

Now multiply 7 with 7 and write in the right side (49)

Answer is 3279

Example 2 Find the square of 58 (58)2

58 X 58 = 3364

Technique:

There are two digits 5 and 8

Add 25 to 8 and write on the left side (32).

Now multiply 8 with 8 and write in the right side (49)

Answer is 3364

Example 3 Find the square of 59 (59)2

59 X 59 = 3481

Technique:

There are two digits 5 and 9

Add 25 to 9 and write on the left side (32).

Now multiply 9 with 9 and write in the right side (49)

Answer is 3381

For squaring other numbers visit multiplication page

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