Square Root of 8100

To find the square root of 8100 we can use both prime factorisation and the long division method. We can also evaluate it mentally if we remember the squares from 1 to 10.

In radical form, the square root of 8100 is written as √8100 where the ‘√’ sign is called the radical sign. In exponential form, it is written as (8100)^½. To find the square root of 8100 we have to find a number whose square is 8100.

Learn more about square and square roots.

What is Square Root of 8100?

The square root of 8100 is a number whose square is 8100. Also, we can say the square root of 8100 is the solution of the equation x² – 8100 = 0 which is ±90. Thus, the square root of 8100 is both 90 and –90, we choose the positive or the negative root as per the requirement of the problem.

How to Find the Square Root of 8100?

Let us find the square root of 8100 using the prime factorisation and long division method. We can also evaluate the square root if we remember the squares from 1 to 100.

Now, 8100 = 81 × 100 = (9 × 9) × (10 × 10)

∴ √8100 = 9 × 10 = 90.

Prime Factorisation Method

To find the square root of 8100 by the prime factorisation method, we first prime factorise 8100 and then make pairs of two to get the square root.

Prime factorisation of 8100 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5

Square root of 8100 = √[2 × 2 × 3 × 3 × 3 × 3 × 5 × 5] = 2 × 3 × 3 × 5 = 90.

Long Division Method

To find the square root of 8100 by the long division method, we shall write 8100 as the dividend and pair its digits from right to left. Now, we shall calculate the square root of 8100 as follows:

To learn how to find the square root of any number long division method, click here.

Video Lessons on Square Roots

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• Square Root 1 to 100
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• Square Root Table
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Solved Examples on Square Root of 8100

Example 1:

Find the volume of a cube whose total surface area is 48600 cm².

Solution:

Let ‘a’ be the length of the sides of the cube.

Total surface area of the cube = 6a² = 48600

⇒ a² = 48600/6 = 8100

⇒ a = √8100 = 90 cm

Volume of a cube = a³ = 729000 cm³.

Example 2:

Find the smallest that must be added to 8000 to make it a perfect square number. Also, find the square root of the perfect square.

Solution:

Now, 89² = 7921 < 8000 < 8100 = 90²

∴ 100 must be added to 8000.

Thus, 8100 is the perfect square number.

The square root of 8100 is 90.

Example 3:

There are 8100 chairs stacked one over another, they have to be arranged such that there are equal numbers of rows and columns of chairs. Find the numbers of rows and columns.

Solution:

Let there be x number of rows and columns, respectively.

The total number of chairs = x² = 8100

⇒ x = √8100 = 90

∴ there are 90 rows and columns.