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 smallest natural number which when added to the difference of squares of 16 and 12 gives a perfect square is ________________ . | |||
| Right Option : A | |||
| View Explanation | |||
The perfect square number between 30 and 40 is: | |||
| Right Option : C | |||
| View Explanation | |||
196 is a perfect square of which number ? | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [10]
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
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Om Umang
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