In this article, we shall learn the values of the square root 1 to 10 with solved examples and practice worksheets. The square root of a number is just the inverse of finding the square root of a number. To determine the square root of any number, we need to find a real number whose square will be the given number. For example, if x2 = y, then the square root of y is ± x.
For any square root 1 to 10, we get two roots: one is positive, and another is negative. The square root of any number in radical form is written as ‘√x’ where the sign ‘√’ is called the radical sign used to represent the nth root of a number. In the exponential form, the square root is written as x1/2 or x0.5.
For square roots 1 to 10:
- Radical form: √a
- Exponential form: a1/2 or a0.5
- Rational or irrational: The square roots of perfect squares are rational numbers or integers, whereas we get an irrational number for the square root of non-perfect square numbers.
- Square from 1 to 10: a2 = a × a
Where a is any number between 1 to 10.
List of Square Roots 1 to 10
The below table lists the square roots 1 to 10 along with their squares.
|
N (1 ≤ N ≤ 10) |
N2 |
√N |
|
1 |
1 |
1 |
|
2 |
4 |
1.414213562 |
|
3 |
9 |
1.732050808 |
|
4 |
16 |
2 |
|
5 |
25 |
2.236067977 |
|
6 |
36 |
2.449489743 |
|
7 |
49 |
2.645751311 |
|
8 |
64 |
2.828427125 |
|
9 |
81 |
3 |
|
10 |
100 |
3.16227766 |
Also Check: List of square roots 1 to 100.
Methods of Finding Square Roots 1 to 10
The square root of any number can be determined by the following method:
- Repeated subtraction method
- Prime factorisation method
- Long division method
- Approximation method
Repeated Subtraction Method
To find the square roots 1 to 10, we have to repeatedly subtract consecutive odd numbers from the given number until we get the answer zero. In the nth step, at which the answer is zero, that value of n is the root of the given number.
Let us try to find the square root of 9
|
Step 1 |
9 |
– |
1 |
= |
8 |
|
Step 2 |
8 |
– |
3 |
= |
5 |
|
Step 3 |
5 |
– |
5 |
= |
0 |
Thus, the square root of 9 is 3.
If we do not get the zero, then the given number is not a perfect square number.
Prime Factorisation Method
To find the square roots 1 to 10 by the prime factorisation method, we shall follow the given steps:
Step 1: Prime factorise the given number.
Step 2: Make pairs of the same prime factors.
Step 3: For each pair, take that factor once out of the radical sign.
Step 4: Lastly, multiply all the factors to obtain the square root.
Let us find the square root of 4 using the prime factorisation method.
Prime factorisation of 4 = 2 × 2
The square root of 4 = √(2 × 2) = 2
This method is mostly used to find the square root of perfect squares. Suppose any factor within the prime factorisation of the number cannot be paired under the radical sign. In that case, the square root of that number cannot be simplified using the prime factorisation method.
Long Division Method
Using the long division method, we can determine the exact value of the square root 1 to 10, whether it is a perfect square or not. For example, the below steps show how to determine the square root of 6 using the division method.
To learn how to find the square root of any number by the long division method, click here.
Approximation Method
To find the square root 1 to 10, we shall use Newton’s formula, which is given as:
|
\(\begin{array}{l}\sqrt{N}=\frac{1}{2}\left [ \frac{N}{A}+A \right ]\end{array} \)
|
Let us try to find the approximate square root of 6 using this method.
Here, N = 6, as 22 = 4 < 6 then A = 2, putting all these values in the formula, we get
Video Lessons on Square Root of a Number
Visualising square roots
Finding Square roots
Related Articles
- Nature of Roots
- Trick to Find Square Root
- Square Root Table
- Square Root Calculator
- Square Root 1 to 25
Solved Examples on Square Root 1 to 10
Example 1:
Find the approximate square root of 7.
Solution:
We can find the approximate square root of 7 using Newton’s formula.
Example 2:
The area of the square is 4 square units. Find the perimeter of the square.
Solution:
Let ‘a’ be the length of the sides of the square.
Area of square = a2 = 4
⇒ a = √4
⇒ a = 2 units (taking the positive root)
Perimeter of square = 4 × 2 = 8 units
Example 3:
Evaluate: √5 + √2 + √6
Solution:
√5 + √2 + √6 = 2.236068 + 1.414213 + 2.449489 = 6.09977
Practice Worksheet on Square Roots 1 to 10
1. Find the square root of 2 using the long division method.
2. Find the square root of 8 using the long division method.
3. Find the square root of 7 using the long division method.
4. Find the approximate value of √5 + 2√9.
5. Evaluate: 4√2 – √6
Frequently Asked Questions on Square Root 1 to 10
What is the value of root 1?
The square root of 1 is ± 1.
What is the perfect square from 1 to 10?
The perfect squares from 1 to 10 are 1, 4, and 9, whose square roots are ± 1, ± 2 and ± 3, respectively.
What is the square root of 6?
The square root of 6 is 2.449489743 (approx.)
Is the square root of 1 to 10 irrational?
Other than the square root of 1, 4, and 9, all the numbers have an irrational square root.
How many square root 1 to 10 are rational?
The square root of 1, 4, and 9 are rational.
