Square Root From 1 To 25

Introduction

The square root of 1 to 25 is a list of the square roots of all numbers from 1 to 25. The square root can have different types of values. Positive integer values for the root from 1 to 25 range from 1 to 5. For an imperfect square, a square root is an irrational number.

The root of any number x is expressed as √𝑥 in radical form and $\mathrm{(x)^{2}}$ in exponential form

Square roots

The square root of any number is the value that can be multiplied by itself to get the original number. The square root is the reverse way to square a number. Therefore, square and square root are associated concepts.

If x is the square root of y, it is expressed as $\mathrm{x\:=\:\sqrt{y}}$. Alternatively, you can also write the original equation as $\mathrm{x^{2}\:=\:\sqrt{y}}$. Here, "√" is the symbol (radical form) used to characterize the square root of a number. Multiplying a number with itself gives the square of that number. The square root of the square of a effective range suggests the unique number.

For example, the square of three is 9, $\mathrm{3^{2}\:=\:9}$, and the square root of 9 is √ 9 = 3. Since 9 is a perfect square, you can easily find the square root. But for imperfect squares such as 3, 7, 5, you have to use other methods to find the square root.

Square roots table 1-25

The table of the square root values of numbers in 1-25 is

Number (x)	Square root of the Number $\mathrm{(\sqrt{X})}$ (Rounded to 3 Decimal Places)
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

Methods to find Square roots

• Method 1 − Prime factorization

Example − $\mathrm{\sqrt{25}}$

The prime factorization of value 25 is $\mathrm{5\times\:5}$

The number which is present twice − 5

Therefore, $\mathrm{\sqrt{25}\:=\:5}$

• Method 2 − Long division approach

Factorisation

The square root of a perfect square number is easily calculated using the factorization method which has been discussed above in details. Let's clear up some examples here −

Number	Prime Factorisation	Square Root
16	$\mathrm{2\times\:2\times\:2\times\:2}$	$\mathrm{\sqrt{16}\:=\:2\times\:2\:=\:4}$
144	$\mathrm{2\times\:2\times\:2\times\:2\times\:3\times\:3}$	$\mathrm{\sqrt{144}\:=\:2\times\:2\times\:3\:=\:12}$
169	$\mathrm{13\times\:13}$	$\mathrm{\sqrt{169}\:=\:13}$
256	$\mathrm{256\:=\:2\times\:2\times\:2\times\:2\times\:2\times\:2\times\:2\times\:2}$	$\mathrm{\sqrt{256}\:=\:(2\times\:2\times\:2\times\:2)\:=\:16}$
576	$\mathrm{576\:=\:2\times\:2\times\:2\times\:2\times\:2\times\:2\times\:3\times\:3}$	$\mathrm{\sqrt{576}\:=\:2\times\:2\times\:2\times\:3\:=\:24}$

Estimation

This method is used as an approximation to guess the value and find the square root.

For example, the square root of 4 is 2, and the square root of 9 is 3, so we can infer that the square root of 5 is between 2 and 3

But you need to take a look at if the value of $\mathrm{\sqrt{5}}$ is close to 2 or 3.

Let’s check the squares of 2.2 and 2.8.

$\mathrm{2.2\:=\:4.84}$

$\mathrm{2.8\:=\:7.84}$

Since the square root of 2.2 is closer to 5, we can estimate that the square root of 5 is equal to about 2.2

Long Division

Finding the square root of an imperfect square is a bit difficult, however it can be calculated using the method which is known as long division. This can be understood with the help of the example under

Solved Examples

1)The vicinity of the square metallic plate is 18 square inches. Find the size of one side of the sheet metal.

Answer −

Let the size of one aspect of the sheet be "a"

Square sheet area $\mathrm{=\:18\:in^{2}\:=\:a^{2}}$

$$\mathrm{i.e.\:a^{2}\:=\:18}$$

$$\mathrm{a\:=\:\sqrt{18}\:=\:4.243\:in}$$

Therefore, metallic sheet Side size 4.243 inches

2)A circular tabletop with an vicinity of 19π square inches. Find the radius of the desk pinnacle in inches?

Answer −

Area on a round countertop $\mathrm{=\:19\pi\:in^{2}\:=\:\pi\:r^{2}}$

, that is, $\mathrm{19\:=\:r^{2}}$ 2 . Therefore, the usage of the values in the radius $\mathrm{=\:\sqrt{19}}$

the table top radius = 4.359 inches.

3) Find the value $\mathrm{6\sqrt{7}\:+\:3\sqrt{7}}$

Answer −

$\mathrm{6\sqrt{7}\:+\:3\sqrt{7}\:=\:6\times\:(2.646)\:+\:3\:\times\:(2.646)\:=\:9\:\times\:2.646[value\:of\:\sqrt{7}\:=\:2.646]}$

Therefore $\mathrm{6\sqrt{7}\:+\:3\sqrt{7}\:=\:9\:\times\:2.646\:=\:23.814}$

Conclusion

In this tutorial, we learned about squares and square roots, mainly square roots of integers from 1 to 25. If the range of a number has a perfect square, then there is a perfect square root in that range. If the number ends with an even number of zeros (0), it can have a square root.

You can multiply the value of two square roots. For example, multiplying $\mathrm{\sqrt{3}}$ by using $\mathrm{\sqrt{2}}$ effects in $\mathrm{\sqrt{6}}$. Multiplying two equal square roots, the end result is the initial number. This means that the result is no longer a square root. For example, multiplying $\mathrm{\sqrt{7}}$ via $\mathrm{\sqrt{7}}$ yields a result of 7. The square root of an irrational number is irrational. A perfect square can't be negative.

FAQs

1. What is the value of the square root from 1 to 25?

The square root value from 1 to 25 is the number 𝑥 when multiplied by itself results in the original number.

It can have different types of values (positive, negative). Between 1 and 25, the square roots of 1, 4, 9, 16, and 25 are integers (rational numbers), whilst the square roots of 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, and 24 are (irrational) decimal numbers that do not stop or repeat.

2. How to calculate the square root from 1 to 25?

There are two usually used ways for calculating square root values from 1 to 25. Prime factorization can be used for perfect squares (1, 4, 9, 16, and 25), and for imperfect squares (2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24) you can use the long division method

3. The square root of which numbers from 1 to 25 lies between 2 and 3?

Values of square roots from 1 to 25 between 2 and 3 are $\mathrm{\sqrt{4}(2)\:,\:\sqrt{5}(2.236)\:,\:\sqrt{6}(2.449)\:,\:\sqrt{7}(2.646)\:,\:\sqrt{8}(2.828)\:,\:\sqrt{9}(3)}$

4. What is the value of the square root 25?

The value of $\mathrm{\sqrt{25}\:is\:5}$

5. Is the range of square roots from 1 to 25 a rational number?

The numbers 1, 4, 9, 16, and 25 are perfect square numbers, so their square roots are integers. Hence, they can be represented in the form of $\mathrm{\frac{p}{q}}$ Where, p and q are coprime integers and $\mathrm{q\neq\:0}$.