Perfect Square
Perfect Square
Square of a number and square numbers:
The square of a number is that number raised to the power 2.
Thus, if a is a number, then the square of a is written as and is given by
That is, the square of a number is obtained by multiplying it by itself
If i.e.
, then we say that the square of number a is number b or the number b is the square of number a.
For example,
so we say that the square of 2 is 4
so we say that the square of 3 is 9
so we say that the square of 12 is 144 etc.
Perfect Square or Square Number:
A natural number n is called a perfect square or a square number if there exist a natural number m such that
In other words, a natural number is a perfect square if it is the square of the same natural number.
Since Therefore, 4 is a square number.
Also,
so 25 is a square number or a perfect square.
so 144 is a square number or a perfect square etc.
STEP I Obtain the natural number.
STEP-II Write the number as a product of prime factors.
STEP III Group the factors in pairs in such a way that both the factors in each pair are equal.
STEP IV See whether some factor is leftover or not. If no factor is left over in grouping, then the given number is a perfect square. Otherwise, it is not a perfect square.
STEP V To obtain the number whose square is the given number take one factor from each group and multiply them.
Illustration: Show that 17640 is not a perfect square.
Solution: Resolving 17640 into prime factors, we have
The area of two square fields are respectively 256 and 625 square meters. The ratio of their sides are : | |||
| Right Option : C | |||
| View Explanation | |||
Which of the following is a perfect square ? | |||
| Right Option : A | |||
| View Explanation | |||
The smallest number by which 136 must be multiplied so that it becomes a perfect square is __________________. | |||
| Right Option : C | |||
| View Explanation | |||
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