How Many Non-Square Numbers Lie Between The Following Pairs of The Numbers 1002 & 1012

Square Numbers

The result of multiplying an integer by itself is known as its square number. A square number is essentially a number formed by the product of two identical integers. The area of a square with 'n' as the side length (where n is an integer) is the best illustration of a square number in geometry.

Definition of Square Number: -

When one integer is multiplied by another integer, the resulting number is known as a square number. When we multiply, for example, (5^2)=5\times 5\ is \ 25

So, we get 25 as a square number. Square numbers can never be negative since multiplying a negative number by another negative number gives a positive number. For example (-5^2)=(-5 \times -5) =25 . So here also we get 25 as the final result

Properties of Square Number: -

• Square numbers will always have the digits 0, 1, 4, 5, 6, and 9 at the ending. For example, 9, 14, 25, 81, and 100 are perfect squares, however, 17, 22, and 83 are not.

• A number with a final digit of 1 or 9 will always have a 1 at the end of its square number. For example, the square number of 9 is 81, while the square number of 11 is 121.

• Square numbers are positive because two negative signs multiplied by them produce a positive sign. For instance, (-5^2)=(-5 \times -5) =25.

• A square number always has an even number of zeros at the conclusion, thus numbers with an odd number of zeros cannot be square numbers. For example, 1600, 3600, and 2500 are square numbers, although 1000, 250, and 160 are not.

• The square of an odd number is always odd, while the square of an even number is always the reason. For example, the square of 15 is 125, while the square of 22 is 484.

• A number with a final digit of 4 or 6 will produce a square number ending in 6. For example; 2 has a square root of 4, and 4 has a square value of 16..

• The square root of a square integer is a whole number. For example, the square root of 441 is 21, hence your 441 is a square number. If the square of a number is a decimal or a fraction, the number is not a perfect square.

Odd and Even Square Integer: -

The following are some interesting facts concerning odd and even square numbers.

• Even integers squares are always even, i.e., 2n^2=4n^2

• Odd integers squares are always odd, i.e., (2n+1)^2=4(n^2+n)+1

Important Points Related to Square Numbers: -

• Square numbers are always whole integers.

• Every square number's square root is always an integer.

• Even integers have squares that are also even.

• Odd integers have squares that are also odd.

Problem Question: -

How many non-square numbers lie between the following pairs of numbers 1002 & 1012 ?

Solution: -

Given that the squares of n and (n + 1) are perfect squares, there are 2n non perfect square integers in between.

Since, there are 200 non-perfect square numbers between 1002 and 1012, 2(100) Equals 200.