For Beginners

Kids,do you know that besides adding, subtracting, multiplying and dividing numbers, there are two other very interesting math operations that are also very useful in many activities? If you wish to know the area of a square or the measures of the sides of a right triangle, two special math operations - getting the square values or getting the square roots of numbers, are some of the more advanced math operations that you must learn.

They are advanced because unlike ordinary multiplication and division, their operations (methods of getting the answers), are much, much more tricky and difficult.

SQUARE OF A NUMBER

Getting the ‘square value’ of a number is like doing a special kind of multiplying a number, in which both the multiplicand and the multiplier are equally the same values. Sometimes, it is described as product of a number multiplied by itself.

Examples:

2 x 2 = 4
27 x 27 = 729
146 x 146 = 21,316

The value 4 is sometimes called the ‘square value’ of 2, or simply, “square of 2”. The same way, 729 is the “square of 27” and 21,316, the “square of 146”. Sometimes, instead of writing 2x2, 27x27 or 146x146, “a small number 2 in upper right side” of a given number is used as a symbol, telling you to multiply that number by itself. So, instead of 2x2, we write 2² = 4 and 27x27 as 27² = 729, while 146x146 as 146² = 21,316.

Maybe, you are wondering why it is called ‘square’. Probably, early mathematicians noticed that the measure of the area of a square is always equal to a certain ‘number multiplied by itself’, so they named it, that way.

SQUARE ROOT

On the other hand, getting the square root of a number, need a very different way, of dividing a number. Unlike in ordinary division at which you need to mention the value of the divisor, in getting the square root of a number, both the divisor and the quotient are unknown and the difficult thing is, both divisor and the quotient must be equally in the same values.

Examples: 36 ÷ 3 = 12 36 ÷ 4 = 9 36 ÷ 6 = 6

In the above examples, 36 can be divided by 3 or 4 but the quotient would not be equal or the same with the divisor. Dividing 36 by 6, we can get a quotient equal to 6, which is the same exact value as to the divisor. In this situation, we can say that 6 is a square root of 36.

In doing this special kind of division, the symbol √ is used before a given number (example √144, read as, “the square root of one hundred forty-four’), to tell you to look for a divisor that will give a quotient, equal to that divisor. Dividing 144 by 12, we come up with a quotient equal to 12 (144 ÷ 12 = 12). Showing equal values for both divisor and quotient we can say then, that √144 = 12.

But there are occasions that the given numbers are in large values (example, √139,876). Getting the square root of such large valued numbers requires a very tedious and tricky method called ‘long hand division’. But as a practice, small valued numbers are introduced for grade school children, to make them easier to memorize.

Easy To Memorize “TABLE OF SQUARE ROOTS”

√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√81 = 9
√100 = 10

PERFECT SQUARES

Not all numbers from 1 to 100 give a square root in whole exact values. Most of them are in decimal values. Below is a list of examples of numbers, having no whole exact square root values:

√ 2, √3, √10, √99 , √28 , √50

Counting from 1 to 100, there are only ten numbers having square roots in ‘exact whole values’ and they are called perfect squares (or simply call them “PERKS”).

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

(Using a calculator, find the square roots of each numbers from 1 to 100 and write down which numbers have an exact whole numbers)

SET OF “PERFECT SQUARES” = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

The above numbers are called Perks because they are squares of whole numbers.

Easy To Memorize “TABLE OF SQUARES”

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100