Learning math is not the easiest thing, but when you like what you are doing and when you are interested in it can make things fun but by learning the first nine tables, you can wake someone up in the middle of the night and they would still be able to recite them. Learn about perfect squares.
What is a perfect squares?
A perfect square is a number obtained when a positive integer is multiplied by itself twice or when a positive integer is squared. For example, 9 is the square of the number three.
The first twenty perfect squares:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, and 400.
All of the above-mentioned numbers are the squares of the positive integers from 1 to 20 respectively. Now there are numerous tips to memorize these, but a lot of people tend to just recite them till the point they remember them like tables. However, one of the most practiced tricks, when you are calculating a square number in your mind, is:
Firstly multiply the 10’s which would be 100
Then multiply the 7’s with the 10’s which would be 140
Now multiply the 7’s which would be 49
Now the last step is to add them which would be the answer 289.
This process might not look simple when written but it is one of the most effective methods to multiply not just squares but big figures easily.
How to Identify a Perfect Square?
The perfect square numbers would end with the digits 0, 1, 4, 5, 6, or 9. If the number ends with the digits 2, 3, 7, or 8 it is simply not a perfect square or a non-perfect square. The numbers ending with 3 or 7 will have 9 as their unit digit, numbers ending with 5 will have 5 as their unit digits, the numbers ending with 4 and 6 will have 6 as their unit digit, and numbers ending with 2and 8, 1 and 9 will have 4, 1 as their unit digits respectively.
However there are quite a lot of exceptions, some of them are:
When you take 10 or 1000 or 100000 into consideration they qualify one rule: they do have 0 in their digit place but they are not squares of any whole number, and how would you eliminate them, it’s simple if the number has an odd number of zeros then it’s not a perfect square. Also not all the numbers ending in 9 are perfect squares, 169 is a square but 159 isn’t, to solve this the number has to qualify another rule which is: whenever the number ends with a 9 in its unit place it should always have an even number in its ten’s digit to be a perfect square, so is the case with the numbers that end with 1 and 4 in their unit digit.
If a number ends with 6, it must and should have an odd number in its ten-digit for it to be a perfect square. Now 225 is a perfect square but 235 is not and how do we know that: every time a number ends with 5 the ten’s digit of the number has to be 2 and will be 2 if it’s a perfect square. And another two additional factors are: if a number is divisible by four, it would leave a remainder of o when divided by 8 for it to be a perfect square.
To go the extra mile the total number of prime factors is always odd for a perfect square.
- Example 1: Let’s consider the number 2371. It has one in unit digit which is a factor but it doesn’t have an even number in the ten’s digit. Hence the number 2371 is not a perfect square.
- Example 2: Let’s consider the number 5776. It also qualifies the first factor because it ends with the number 6 and it also passes the second factor which is the ten’s digit being an odd number, so the number 5776 is a perfect square, if you are still not sure you can always use the prime factorization rule.
That was all about perfect squares from 1to 200 or the first twenty perfect squares, how to get a perfect square, how to identify a perfect square and some examples. Calculating perfect squares isn’t a tough task, you can use the trick mentioned in the article to calculate it faster in your mind and get it correct almost all of the time.
Frequently Asked Questions
- What are the first thirty perfect squares?
A perfect square is a number obtained when a whole positive integer is multiplied by itself or squared, with that being said the first 30 perfect squares are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361,400, 441, 484, 529, 576, 625, 676, 729, 784, 841 and 900.
- Is it very necessary to memorize the first twenty perfect squares?
A math teacher or a professor would say yes, but a student doesn’t need to memorize the first twenty squares, you can always calculate them as long as you have the 1-9 tables in your hand, but when you are in a hurry during a test the memory might come in handy, it’s not hard one can memorize then pretty easily if tried.
- How to describe a perfect square?
The school definition for a perfect square is “A number which is the result of squaring a whole number is called a perfect square”. It can be described by its definition or even simple words like “A number when multiplied by itself gives us a perfect square”.
- Is the number 400 a perfect square?
Yes, the number 400 is a perfect square, it passes all the factors that determine a number as a perfect square such as having 0, 1, 4, 5, 6, or 9 in unit’s digit and if it has a zero it must have even number of zeros and 400 does have even number of zeros, hence it is a perfect square, its root is 20.