Understanding the square roots from 1 to 30 is important in mathematics. Square roots are key concepts used in algebra, geometry, and solving real-world problems. This guide breaks down the square roots from 1 to 30. It includes a square roots chart, a list of square roots, and methods for calculating them. It also distinguishes between perfect square numbers and non-perfect squares in this range.
Table of Contents
The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 9 is 3 because 3 × 3 equals 9. Square roots can be perfect or non-perfect. Knowing both types helps master math operations from 1 to 30.
This list of square roots offers a quick reference to square root values from 1 to 30. It includes both perfect squares and non-perfect squares.
Radical Form |
Approx. Square Root Value |
1 |
1.000 |
2 |
1.414 |
3 |
1.732 |
4 |
2.000 |
5 |
2.236 |
6 |
2.449 |
7 |
2.646 |
8 |
2.828 |
9 |
3.000 |
10 |
3.162 |
11 |
3.317 |
12 |
3.464 |
13 |
3.606 |
14 |
3.742 |
15 |
3.873 |
16 |
4.000 |
17 |
4.123 |
18 |
4.243 |
19 |
4.359 |
20 |
4.472 |
21 |
4.583 |
22 |
4.690 |
23 |
4.796 |
24 |
4.899 |
25 |
5.000 |
26 |
5.099 |
27 |
5.196 |
28 |
5.291 |
29 |
5.385 |
30 |
5.477 |
Use this individual list of square roots as a study reference or for calculation. Whether you're identifying perfect square numbers or estimating square root values, this breakdown of square root 1 to 30 will help you understand and apply these numbers accurately.
A perfect square is a number that is the square of an integer. In other words, when an integer is multiplied by itself, the result is a perfect square. The square root of a perfect square is always a whole number.
Here are the square root values for perfect square numbers between 1 and 30:
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
These roots are whole numbers and do not need further approximation.
A non-perfect square is a number that cannot be expressed as the square of a whole number. In other words, their square root values are irrational, meaning the decimals go on without repeating.
Here’s a list of square roots from 1 to 30 that are non-perfect squares with approximate values up to three decimal places:
Number |
Square Root (Approx.) |
2 |
2≈1.414 |
3 |
3≈1.732 |
5 |
5≈2.236 |
6 |
6≈2.449 |
7 |
7≈2.646 |
8 |
8≈2.828 |
10 |
10≈3.162 |
11 |
11≈3.317 |
12 |
12≈3.464 |
13 |
13≈3.606 |
14 |
14≈3.742 |
15 |
15≈3.873 |
17 |
17≈4.123
|
18 |
18≈4.243 |
19 |
19≈4.359 |
20 |
20≈4.472 |
21 |
21≈4.583 |
22 |
22≈4.690 |
23 |
23≈4.796 |
24 |
24≈4.899 |
26 |
26≈5.099 |
27 |
27≈5.196 |
28 |
28≈5.291 |
29 |
29≈5.385 |
30 |
30≈5.477 |
These values in the square roots chart are approximated to three decimal places and used in daily mathematical applications. Since these are not perfect square numbers, you can’t simplify them to whole numbers.
Each square root from 1 to 30 can be shown in both radical and exponential forms:
Square Root in Radical Form
The symbol √ is called the radical sign.
Writing a means “the square root of a”.
Examples:
25=5
4=2
2≈1.414(This is an irrational number because its value cannot be expressed exactly, only approximately as 1.414…)
Radical form is simple and often used in basic arithmetic.
Square Root in Exponential Form
In mathematics, roots can also be expressed using exponents (powers).
The rule is:
a=a12
Examples:
25=2512=5
4=412=2
2=212
Here, the exponent 1/2 means “take the square root.”
This form is very useful in algebra and higher classes because it is easier to apply the rules of exponents than radicals. Using both forms helps in understanding how to represent square root values flexibly.
Example 3: Simplify 36+9
Solution:
We know:
36=6,9=3
So substituting the value in the given expression, we get,,
36+9=6+3=9
Hence, the value is 9.
Example 4: Find the value of 52 (non-perfect square).
Solution:
We know:
2≈1.414
So substituting the value in the given expression, we get,,
52=5×1.414=7.07
Hence, the value of 52 is approximately 7.07.
Example 5: Which two integers does 17 lie between?
17≈4.123
16=4and 25=5
So, 17 lies between 4 and 5
Understanding the square roots from 1 to 30 is basic for further math learning. This guide explained perfect square numbers, included a full square roots chart, and showed how to find square roots using prime factorization and long division. Whether you're looking for a list of square roots, learning to estimate square root values, or exploring their different forms, mastering this topic gives you an advantage in both school and real-world math.
Answer: The value of 3 (square root of 3) is approximately 1.732. It is an irrational number and cannot be expressed exactly as a simple fraction.
Answer: The value of 2 (square root of 2) is approximately 1.414. Like 3, it is also an irrational number.
Answer: To solve or estimate 3 manually, you can use methods like long division, approximation, or a calculator. One way to estimate is by trying successive squares:
For example,
1.7² = 2.89
1.73² = 2.9929
1.732² ≈ 3.0001 → So 3≈1.732
Answer: The value of 5 (square root of 5) is approximately 2.236. You can find it using a calculator or by estimation methods similar to those used for 3.
Learn square roots from 1 to 30 the easy way with charts and tips at Orchids The International School!
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