What is a Square of a Number?
Are you someone who is looking to understand what squares and square roots of a number are? or are you someone who is struggling to understand the difference between twice of a number and square of a number? If yes, then Vedantu has brought Square Root from 1 to 25 - Value Table, Calculating Method, Solved Examples & FAQs to solve your confusion and to answer all your questions. Let’s start by understanding the meaning of a square of a number.
When a number is multiplied by itself, the product is called the square of that number.
The square of a number is expressed as the number to the power 2 and it is pronounced as squared off a number.
Like this:
22 = 4 pronounced as 2 squared
And read as 2 squared equals 4
For Example,
2 x 2 = 4 or 22 = 4. Thus, the square of 2 is 4.
Similarly, 3 x 3 = 9 or 32 = 9,
4 x 4 = 16 or 42 = 16,
5 x 5 = 25 or 52 = 25, etc.
Square numbers are also called perfect squares.
A Natural number is said to be a perfect square if it is the square of another natural number.
For ex., 5 x5 = 52 = 25, 6 x 6 = 62 = 36, 7 x7 = 72= 49, etc.
So we can say that 4, 9, 16, 25, 36, ……. are all perfect squares.
Squares Up to 30
The table below shows the values for squares 1 to 30. Memorizing squares from 1 to 30 will help you to simplify your problems more quickly.
Properties of Square Numbers:
In 1 to 30 squares you notice that a number ending with 2, 3, 7 or 8 can never be a perfect square.
At the end of a perfect square, the number of zeros is always even.
The Square of an even number is always even and the square of an odd number is always odd.
The Square of any real number always remains positive.
Methods of Finding the Squares:
Square of a number can be found in two ways
Column method
Diagonal method
Square Roots
The square root of a number x is that number which when multiplied by itself gives the number x itself. The number x under consideration is a perfect square.
For Example, 22 =4, or the square root of 4 is 2
32 =9, or the square root of 9 is 3
42 = 16, or the square root of 16 is 4
The symbol of the square root is \[ \sqrt{}\]
Thus, the square root of 4 is represented as \[ \sqrt{4}\] = 2 and that of 9 is represented as \[ \sqrt{9}\] = 3 and so on.
Just as the division is the inverse operation of multiplication, the square root is the inverse operation of squaring a number.
Note: Every square number can have a positive or negative square root.
Square Root 1 to 30
Square Roots 1 to 30 will help you to solve the most time consuming long equations within no time, Square roots of 1 to 25 are listed in the table below.
Properties of Square Root:
If the unit digit of a number is 2,3, 7 and 8 then it does not have a square root in natural numbers.
If a number ends in an odd number of zeros, then it does not have a square root in natural numbers.
The square root of an even number is even and that of an odd number is odd.
Negative numbers have no squares root in a set of real numbers.
Methods of Finding the Squares Roots:
Square of a number can be found in two ways
Prime Factorisation Method
Long Division method
Solved Examples:
These solved examples are provided for you to understand the steps of the solutions. You are expected to follow a similar pattern in the exam while solving the questions. Also, these examples will help you understand how the concepts are applied in practice.
1. Find the value of √144 by the prime factorization method.
Ans:
Step 1: express 144 in prime factors
144 = 24 x 32
Step 2: Split the prime factors in two equal groups
144 = ( 23 x 3) x (23 x 3)
=(23 x 3)3 = 12
2. The area of a square is 1521 cm2. Find the length of a side of the square by the prime factorisation method.
Ans: Area of square = length x breadth
Therefore, Length of the square = √area
Now, 1521 = 32 x 132
= (3 x 13) (3 x 13)
= (3 x 13)2
Therefore, \[ \sqrt{1521}\] = 3 x 13 = 39
The length of a side of the square is 39 cm.
Quiz Time:
These questions will help you test your understanding of the concepts. Answers to these questions are not provided on purpose. You will have to use your brains and find them on your own. This exercise will help you to become self-reliant. If the need arises, you can seek reference from the above-solved questions
The area of a square is 7225 cm2. Find the length of a side of the square by prime factorisation.
Find the square root of 676 using the prime factorisation method and the long division method. Verify that the answer in both cases is the same.
The area of a square tin plate is 7056 cm2. Find the length of a side of the plate.
Can 8100 be a square number? Why or why not?
FAQs on Square Root from 1 to 25
1. Can square root from 1 to 25 help me in the exams?
Yes, Square Root from 1 to 25 can surely help you in the exams. You will come across direct questions for calculating the square roots of these numbers. You may also encounter questions where you will be expected to use the square roots of these numbers to reach the final answer. For example, in the Pythagoras theorem, you will be using square and square roots of numbers. To solve such problems knowing square roots will come in handy. We suggest you at least practice questions enough times to get yourself acquainted with square roots from 1 to 25.
2. Can square root from 1 to 25 help me in competitive exams?
You will encounter many problems in competitive exams which will require you to know basic numeracy and quant. You will also be expected to know Square Root from 1 to 25. the questions will not be asked directly, rather they will form part of the solutions. For example, while solving a quadratic equation you may use square roots. Quadratic equations based questions are prominently seen in the banking exams. You will also have questions enrooted in trigonometric functions and Pythagoras theorem, here also knowledge of square roots will come to your rescue.
3. Do I need to memorize all the squares in Square Root from 1 to 25?
Vedantu jas provided you with ways of calculating square roots, you can use that. But if you are in a hurry then remembering Square Root from 1 to 25 can save you a lot of time. We suggest first you understand the meaning of square root then focus on understanding the method of calculation. Follow this exercise with solving various problems on square roots wherein you will be required to find square roots of 1-25 multiple times. Solving many such questions will automatically help you in remembering the square roots, without you putting in extra efforts to remember every square root.
4. What topics are discussed in Square Root from 1 to 25?
The topic of Square Root from 1 to 25 are covered in a very holistic way. Vedantu has tried to cover every topic in great detail for you. Topics covered include the definition of the square of a number, values of squares from 1-30, methods of calculating squares, the meaning of square roots, values of square roots from 1-30, methods of calculating square roots of a number, properties of square roots, solved examples, quiz questions for you to test your understanding, etc.
5. Why should I prefer Square Root from 1 to 25 by Vedantu?
On the internet, you will find many websites giving you a list of values of squares and square roots of numbers. But Vedantu also gives you ways of calculating Square Root from 1 to 25. all the methods mentioned in the study materials are made available to you by subject matter experts themselves who have a very deep understanding of the subject. Vedantu has also provided you with several examples to understand every method. Towards the end, you have been given questions for self-analysis. All this makes Vedantu a preferred choice among the students.
6. Is 1 a Square Number?
Yes. When you multiply a number by itself we get the product as a Square number. Hence if we multiply 1 by itself we get 1, i.e 1 x 1 = 1.
1 is called a square number because it gives the area of a square with side length as an integer.
We can express it as a x a = a2 i.e 1 x 1 = 12 = 1.
7. What is Perfect Square?
A product of an integer with itself is said to be square or perfect square. or in other words, you can say that if any number is multiplied by itself it gives a perfect square.
For example, 25 is a perfect square since it can be written as 25 = 5 x 5.
A perfect square is a number obtained by squaring two equal integers.
For testing, if a given number is a perfect square or not we write the given number as the product of prime factors then we make pairs of the same factors. If there are factors all of which have a pair, then the given number is a perfect square.