Vedic Maths

Tuesday, March 4, 2014

Squaring Any Two-Digit Number Whose Tens Digit IS 5

Rule: Add the units digit to 25 and affix the square of the units digit to the result. If the square of the units digit is a one-digit number, precede it with a 0.

Find the square of 53, using this method.

First, add the units digit, 3 to 25.

25 + 3 = 28

Next, affix the square of the units digit to the result.

3 X 3 = 9

Since the answer is a one-digit number, place a zero in front of 9 before affixing it to the 28.

2,809 Answer

As another example, find the square of 57.
Again, the units digit is added to 25.

25 + 7 = 32

Next,square the units digit

7 X 7 = 49

and affix to the previous result.

3,249 Answer

This time the square of the units digit was a two-digit number, and therefore it was not necessary to precede it with a zero.

Saturday, March 1, 2014

Squaring Any Three-Digit Number Ending IN 25

The square of 25 is 625. Oddly enough, these are the last three digits in the square of any three-digit number ending in 25. Since squaring a three-digit number results in at most six digits, the problem here is merely to find the first three digits of the answer.

Rule: The First two digits (that is, the hundred-thousands digit and the ten- thousands digit) are found by squaring the hundreds digit of the given number and adding to the result one-half the hundreds digit of the given number (ignoring the fraction 1/2 if it occurs). If the result is a one-digit number, then there is no hundred-thousands digit in the answer and the result is the ten-thousands digit of the answer. The thousands digit of the answer is 5 if the hundreds digit of the given number is odd and 0 if the hundreds digit of the given number is even, Affix 625 to obtain the final answer.

Two illustrative examples will be used to demonstrate the ease with which this short cut may be used.

Example:

Square 225.

First, square the hundreds digit of the given number, to obtain

4

To this add one-half the hundreds digit of the given number.

4 + 1 = 5

Since the answer is a one-digit number, 5 is the ten-thousands digit of the answer. The thousands digit of the answer will be 0, since the hundreds digit of the given number, 2, is even. To this we affix 625 to obtain the final answer.

50,625 Answer

Squaring Any Number Ending IN 5

SQUARING ANY NUMBER ENDING IN 5

Rule: Multiply the complete number to the left of the 5 by one more then itself and affix 25 to the result.

To demonstrate, we shall find the square of 195. The complete number to the left of the 5 is 19. Raising this one number high gives us 20.

20 X 19 = 380

To which 25 is affixed.

38,025 Answer

Squaring Any Number Ending IN 1

SQUARING ANY NUMBER ENDING IN 1:

Rule: First,square the number to the left of the units digit. Then double the number to the left of the digit. Affix the units digit of this result to the square found in first step. If the result is more than 9, add the part to the left of the units digit to the square found in the first step. The units digit of the answer is always 1.

Consider the following example: Square 251.

The number to the left of the 1 is 25. we know the square of 25 is 625. Next, twice 25 is 50. affix the zero in 50 to 625.

625 + 5 = 630

To which are affixed the 0 and the units digit (which is always 1).

63,001 Answer

Wednesday, February 26, 2014

Squaring Numbers

When we speak of "squaring" a number,we mean multiplying the number by itself. To square 23 we write.

23 X 23 (or commonly 23 sq.)

The process of multiplying a number by itself follows a systematic pattern which lends itself readily to short-cut methods. The simple rules explained in this blog cover an amazingly wide range of numbers. Most of the shortcut included here involve two-digit numbers, but a few involve three - and four-digit numbers. With a little ingenuity,number of any size can be squared easily,used the short cuts that follow as the basis for many others. But there is a law of diminishing returns in using larger numbers; then, instead of saving time and labour, the short cut becomes merely a "stunt".