Square Root 1 to 30 (Definition, Examples) - BYJUS

Square Root 1 to 30

The square root of a number is another number which when multiplied by itself results in the original number. Having an understanding of square roots can help us solve math problems faster and more efficiently. In this article, we are going to learn about the square roots of numbers from 1 to 30....Read MoreRead Less

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What is the Square Root of a Number?

The square root of a number is a number that when multiplied by itself, gives the original number. Every number has two square roots, both having the same absolute value, but one of the square roots is positive and the other is negative. 

 

A radical sign ‘\(\sqrt{~~}\)’ is used to represent the square root in a math equation and the number that is written under this sign is known as the radicand. A number is said to be a perfect square if its square root is an integer. A number is said to be an imperfect square if its square root is not an integer.

Square Root of Numbers from 1 to 30

The following table shows the square roots of numbers from 1 to 30. Let’s go through it and try to remember them well.

 

 

sqr1to30

 

Remembering these square root values can come in handy as it can help in solving math problems that involve applying the square root of different numbers ranging from 1 to 30.

How do we Calculate the Square Root of a Number?

The square root of a number is calculated by two different methods.

 

  • Prime Factorization Method

As the name suggests, prime factorization is the process of writing a number as a product of its prime factors. Prime numbers are numbers that have only two factors, that is 1 and the number itself. We can use the prime factorization method to find the square roots of perfect squares.

 

Example: Find the value of \(\sqrt{25}\).

 

Prime factorization of 25 is written as 5 x 5

Pairing prime factors = 5

 

Hence, the square root of 25 is 5.

 

  • Long Division Method

The square roots of imperfect square numbers can be determined using the long division method. You will study this method in detail in higher grades.

Solved Examples

Example 1:

Evaluate the expression 7\(\sqrt{21}\) + 9\(\sqrt{19}\) ? (Write the answer with up to two decimal places).

 

Solution:

Given expression is 7\(\sqrt{21}\) + 9\(\sqrt{19}\)

 

\(\Rightarrow\) 7 x 4.58 + 9 x 4.36      [Substitute 21 = 4.58 and 19 = 4.36]

 

\(\Rightarrow\) 32.06 + 39.24             [Multiply]

 

\(\Rightarrow\) 71.3                             [Add]

 

Thus, 7\(\sqrt{21}\) + 9\(\sqrt{19}\) = 71.3

 

Example 2:

John decided to run in Greek Rock Park every morning as his daily exercise routine. If the jogging track is circular and has an area of 298 square meters then find its radius. [Take Π = 3.14]

 

Solution:

As mentioned, the area of the jogging track, A = 298 m\(^2\)

 

The radius of the ground can be calculated by using the formula for the area of a circle: 

 

A = r\(^2\)

 

298 = 3.14 x r\(^2\)         [Substitute the values in the formula]

 

\(\frac{298}{3.14}\) = r\(^2\)                   [Divide both sides by 3.14]

 

\(\frac{298}{3.14}\) x \(\frac{2100}{100}\) = r\(^2\)        [Multiply and divide by 100]

 

\(\frac{29800}{314}\) = r\(^2\)                 [Simplify]

 

94.9 = r\(^2\)                  [Simplify]

 

\(\sqrt{94.9}\) = r                 [Square root on both sides]

 

9.74 = r                     [Simplify]

 

r = 9.74 m

Therefore, the radius of the jogging track is 9. 74 meters.

 

Example 3:

Mindy baked a cylindrical cake for her friend’s birthday. What is the radius of the cake if its height is 25 cm and volume is 1570 cm\(^3\)? [Take Π = 3.14]

 

Solution:

Given the height of the cake, h = 25 cm, and the volume of the cake, V = 1570 cm\(^3\).

 

We can use the formula for the volume of a cylinder to find the radius: 

 

V = r\(^2\)h

 

1570 = 3.14 x r\(^2\) x 25      [Substitute the given values in the formula]

 

1570 = 78.5 x r\(^2\)             [Multiply]

 

\(\frac{1570}{78.5}\)= r\(^2\)                          [Divide both sides by 78.5]

 

\(\frac{1570}{78.5}\) x \(\frac{10}{10}\) = r\(^2\)                 [Multiplying and dividing by 10]

 

\(\frac{15700}{785}\) = r\(^2\)                        [Simplify]

 

20 = r\(^2\)                            [Simplify further]

 

20 = r                              [Square root on both sides]

 

4.472 = r                          [Simplify]

 

r = 4.472 cm

 

Hence, the radius of the cake is \(\sqrt{20}\) centimeters or 4.472 centimeters.

Frequently Asked Questions

Learning square roots is important in math as we use square roots to perform calculations like normal distributions, the quadratic formula, Pythagorean theorem, and finding aspects of geometric shapes. Not just math, square roots are often used in physics.

From the square root of 1 to 30 chart, we can see that the square root of 24 is 4.8989.

Yes, 25 is a perfect square number as its square root is an integer.

The perfect squares from 1 to 30 are 1, 4, 9, 16, and 25.