An Introduction to Square Root
The square root of a number is the value obtained by raising the number to the power ½. The number obtained by multiplying a number by itself is called a square number. Square and square roots are inverse Mathematical operations. Squares and square roots are used generally in solving quadratic equations and many other Mathematical calculations. Square root is denoted by a symbol ‘√’. Square root of a number ‘x’ is written as √x or x½. Square root of any number has two values: one positive and one negative. However, the magnitude of both the values remain the same.
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Value of Root 1 = +1 or -1
Significant Facts About ‘1’
1 is the most important element of Mathematics. One or unity in Mathematics is used to represent a single entity in a number, measurement, or calculation. The number ‘1’ has a few peculiar properties which are very important in Mathematical calculations. They are:
‘1’ is the number used to represent a single identity.
‘1’ is added to any integer to get the immediate successive integer.
When ‘1’ is subtracted from any integer, the immediately preceding integer is obtained.
1 is the multiplicative identity of any number. i.e. When any number is multiplied by itself, the number itself is obtained as the product.
The multiplicative inverse of any number is the value obtained when ‘1’ is divided by the number.
When any number is divided by ‘1’, the answer is the number itself.
When the number is divided by itself, the answer obtained is one.
The value of any number raised to the power zero is equal to unity.
Square Root of +1
It is very important to know how to find the square root of 1 because it gives a clear understanding of finding the square root of other integers. A positive value of one can be written as \[1 \times 1 or 1^{2}\].
So, square root of 1 can be calculated as:
\[\sqrt{1} = \sqrt{1^{2}} = \pm 1\]
The formula for finding the roots of a quadratic equation can also be used to find the square root of 1.
Let the square of the number ‘x’ be equal to ‘1’. This can be written as:
\[x^{2} = 1\]
\[x = \sqrt{1}\] → (1)
The above equation is a quadratic equation which can be represented in standard form as:
\[x^{2} + 0 x - 1 = 0\]
The above equation is of the form ax2 + bx + c = 0. So, a = 1, b = 0 and c = -1.
The value of ‘x’ can be found using the formula:
\[x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} \]
\[x = \frac{-0 \pm \sqrt{0^{2} - 4x \times 1 \times -1}}{2 \times 1} = \pm \frac{\sqrt{4}}{2} =\pm \frac{2}{2} \rightarrow (2)\]
Comparing equations (1) and (2), we can infer that the value of under root 1 is equal to either positive or negative unity.
Value of root 1 = \[\pm\] 1
Most commonly, the value of under root 1 is taken as positive unity or + 1.
Value of Square Root of -1
Root value of ‘-1’ does not exist in theory. It is an imaginary number represented as ‘i’. Root of -1 is generally used to represent complex numbers which include both the real part and the imaginary part. With the knowledge of the square root of negative unity, the root value of any negative number can be found. Square root of -1 is a positive or negative imaginary unit ‘i’. However, in most cases, the value of the root of -1 is taken as a positive imaginary unit ‘i’.
Square Root of First 30 Integers:
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Square root 1 to 10:
Values of Square Root 1 to 10 is Listed in the Table Below:
These values of square root 1 to 10 are depicted on the number line as a square root spiral.
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Example Problems:
1. Solve for p if \[p^{2} + 8 = 3\]
Solution:
\[p^{2} + 8 = 3\]
\[p^{2} = 3 - 8 \]
\[p^{2} = - 5 \]
\[p = \sqrt{-5} = \sqrt{-1} . \sqrt{5} \]
\[p = \sqrt{5i}\]
2. Find the value of \[7\sqrt{1} - 5\sqrt{1} + 2\sqrt{1}\] using the value of under root 1.
Solution:
Value of \[\sqrt{1} = 1\]
\[7\sqrt{1} - 5\sqrt{1} + 2\sqrt{1}\]
= 7 (1) - 5 (1) + 2 (1)
= 7 - 5 + 2 = 4.
Fun Facts:
‘I’ is the first unit of imaginary numbers. It is equivalent to number ‘1’ in real numbers.
When negative unity is raised to the power of odd numbers the answer is -1 and when negative unity is raised to the power of even numbers, the answer is + 1.
The value of root 1 to any power is equal to 1.
Significance of Square Roots
In the applied area of Mathematics, the concept of square roots is considered to be highly important. The concept lays the basic foundation for algebra. Students who plan to score exceptionally in the subject should study this chapter in detail.
Vedantu tries to explain complex concepts in simple terms. It makes it convenient for the students to dive deeper into the logical reasoning behind the numerical values. There are many benefits for studying square roots-
Square roots from basic to complex hold a significant weightage in board exams.
The tricks related to calculating the square roots help in setting the mind map for mastering Math.
It further helps in taking your mathematical skills to the level of abstraction.
With the help of square roots, students will be able to hone their calculative skills in an intelligent manner.
Besides being important in the concept of algebra, square roots play a significant role in boosting your child's theoretical and statistical methods.
In addition to Math, square roots would help you to get a better understanding of some important laws in Physics.
Learn Square Roots Easily
Square roots might seem to be complicated at times. With Vedantu, Students can clear all their doubts related to it.
In order to make the concept easy, we provide sample problems at the right intervals. You can easily get a firm grip over the topics that are considered to be of main importance in solving algebra.
To start with, students should understand the definition of the concept as defined by the Vedantu experts. The definition is formulated by the experts and will stick with you in the long run.
Before coming to the other numbers, it is important that you take one step at a time. Starting from Number 1, Vedantu has covered all the details related to its value, method and example problems to help you score well on the topic.
Vedantu provides a detailed tabular representation for the square root of the first 30 integers. It also provides a table consisting of values from 1 to 10.
Experts at Vedantu make sure to include all the concepts for the particular topic you are looking for. Along with the square root of +1, it has also covered the square root of -1. Questions related to it are most likely to be asked in the exams. It helps you in scoring well on the 'High-order thinking skills(HOTS).
To make sure that students have fun during their learning process, Vedantu consists of 'fun facts'
related to the topic. Students from all the classes find it intriguing and curious enough to know more about the concept.
To score well in Mathematics, it is very important to keep practicing the example problems. Vedantu experts have formulated some important examples along with the solutions. It will help you in understanding the kind of questions expected out of the topic.
FAQs on Square Root of 1
1. What are Squares and Square Roots?
Square of a number is the value obtained when a number is multiplied by itself once. Square of a number is the number raised to the power 2. Square of a number ‘x’ is represented as ‘x2’. Square root of a number is that value which when multiplied by itself gives the number as the product. Square root of a number ‘x’ is denoted as ‘√x’ or ‘x1/2’. Perfect square numbers are those numbers that have an integer value as their square roots. Every number has two square roots: a positive and a negative root. In most of the cases, the positive roots are taken into account.
2. What is the Value of Root 1?
Square root of any number is the number raised to the power ½. Square root of the positive value of 1 is either a positive value of 1 or negative value of 1. This is true because, 1 x 1 = 1 and -1 x -1 = 1. Square root of the negative value of one does not exist in theory. However, the square root of -1 is considered to be an imaginary number unit ‘i’. Square root of -1 is either a positive value of ‘i’ or negative value of ‘i’. Imaginary roots of unity are used in representing complex numbers and in calculations involving complex numbers.
3. How can I simplify the Square Roots?
While learning the concept of square roots, it is very important for you to understand the rules of simplifying the square roots. It will help you in avoiding the complexities involved in the topic. The first step to this is- factorization. Vedantu provides all the information about the concept in detail. Students can use this method for square roots in the same way as they were taught to apply this method for ordinary numbers. In simple terms, you just need to break the factors and then check if you can split it anymore. This method saves a lot of your time and helps you in scoring well on your exam.
4. Are graphs important for understanding Square Roots?
Graphical representations are an important part of the concepts related to squares and square roots. It will make your learning more creative and fun. In addition, graphs hold a significant weightage in your exams. Students can expect to find questions based majorly on their representation and knowledge of graphs. With the help of Vedantu, students can easily practice their solutions using graphs. The website also provides a lot of sample problems and their solutions formulated by the subject experts. Practice your graph skills well and get ready to be at the top of your class.
5. Is Vedantu useful in understanding Square roots?
Vedantu is an online learning platform that helps students to score well on their exams by compiling all the important resources in one place. For Mathematics, Experts at Vedantu simplify the concepts and support them with a lot of practice questions along with their standardized solutions. For the concept of square roots, Vedantu gives a precise definition at the beginning which is then followed by a detailed explanation of the topic. To make the learning process more interesting, it also adds 'fun facts' and 'important points to note' in the middle of the exercises.
6. Are there different methods to find the square roots of the numbers?
Mathematics is a vast subject. While exploring the new concepts included with the subject, it is very important to guide your children in the right direction. There can be many methods to find the solution to a certain problem. The same applies to the concept of square roots. There are four methods to take out the square roots of numbers. However, it is recommended to stick to the method which suits you the best. Practice is an essential component in order to improve your scores. Regularly practice and master the method you choose. Do notice that the answers might have a slight difference depending on if the numbers are perfect squares or not.
7. What are perfect Squares?
Perfect Squares are taken out by multiplying the two integers that are equal to each other. For instance- the number 4 is considered as a perfect square because it can be derived by multiplying the two equal integers i.e 2 × 2 = 4. For another instance, the number 25 is a perfect square as 5 × 5 = 25.
Vedantu explains the concept of 'perfect squares' in detail. It covers all the points you need to score well in your exams. You can easily find out if the number is a perfect square by taking out its square roots. For instance- The number 26 is not a perfect square as its square root is not a whole integer.