Is 900 a square of an even number?

The short answer is yes, 900 is the square of an even number. Specifically, 900 = 30^2, where 30 is an even number. Let’s break this down step-by-step.

Table of Contents

Understanding Squares and Square Roots

A square number is a number obtained by multiplying a number by itself. For example:

2 x 2 = 4, so 4 is a square number
3 x 3 = 9, so 9 is a square number
5 x 5 = 25, so 25 is a square number

The number that is multiplied by itself to obtain a square number is called the square root. For example:

The square root of 4 is 2, because 2 x 2 = 4
The square root of 9 is 3, because 3 x 3 = 9

The square root of 25 is 5, because 5 x 5 = 25

So in general:

If n is a square number, its square root is the number that when multiplied by itself equals n.

Determining if a Number is Even or Odd

A number is even if it is divisible by 2 with no remainder. Some examples of even numbers:

A number is odd if dividing it by 2 leaves a remainder of 1. Some examples of odd numbers:

So to determine if a number is even or odd:

If the number divided by 2 has a remainder of 0, it is even
If the number divided by 2 has a remainder of 1, it is odd

Is 900 a Perfect Square?

Now let’s examine the number 900. Is it a perfect square, meaning is there a number that when multiplied by itself equals 900?

Let’s try taking the square root of 900 using a calculator:

√900 = 30

This tells us that 30 x 30 = 900. Therefore, 900 is a perfect square, and its square root is 30.

Is 30 Even or Odd?

We determined that the square root of 900 is 30. Now we just need to determine if 30 is even or odd.

When we divide 30 by 2, the remainder is 0. Therefore, 30 is an even number.

In summary:

900 is a perfect square
The square root of 900 is 30

30 is an even number

Conclusion

Since 900 is a perfect square, and its square root 30 is an even number, we can conclude that 900 is the square of an even number.

The full logic is:

900 is a perfect square
The square root of 900 is 30
30 is an even number

Therefore, 900 is the square of the even number 30

So in summary, yes, 900 is the square of the even number 30. This step-by-step analysis shows that 900 satisfies the requirement of being a square of an even number.