Square Root of 2500

To find the square root of 2500, we can use both prime factorisation and the long division method. If we have the knowledge of squares from 1 to 10, we can also calculate the square root of 2500 mentally. In radical form, the square root of 2500 is written as √2500, where the ‘√’ sign is called the radical sign. In exponential form, it is written as (2500)^½. To find the square root of 2500, we have to find a number whose square is 2500.

Learn more about square and square roots.

What is Square Root of 2500?

The square root of 2500 is a number whose square is 2500. Now, if we square both 50 and –50 we get the answer 2500. Thus, the square root of 2500 is both 50 and –50, we choose the positive or the negative root as per the requirement of the problem.

How to Find the Square Root of 2500?

Let us find the square root of 2500 using the prime factorisation and long division method. We can even calculate the square root if we remember the squares from 1 to 100.

Now, 2500 = 25 × 100 = 5 × 5 × 10 × 10

∴ √2500 = 5 × 10 = 50.

Prime Factorisation Method

To find the square root of 2500 by the prime factorisation method, we first prime factorise 2500 and then make pairs of two to get the square root.

Prime factorisation of 2500 = 2 × 2 × 5 × 5 × 5 × 5

Square root of 2500 = √[2 × 2 × 5 × 5 × 5 × 5] = 2 × 5 × 5 = 50.

Long Division Method

To find the square root of 2500 by the long division method, we shall write 2500 as the dividend and pair its digits from right to left. Now, we shall calculate the square root as follows:

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

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Related Articles

• Square Root 1 to 100
• Trick to Find Square Root
• Square Root Table
• Square Root Calculator

Solved Examples on Square Root of 2500

Example 1:

Find the cost of fencing a square park whose area is 2500 m² and the cost of fencing per 10 m is ₹ 700.

Solution:

Let ‘a’ be the length of the sides of the square park.

Area of the square park = a² = 2500

⇒ a = √2500

⇒ a = 50 m

Perimeter of the park = 4a = 4 × 50 = 200 m

Cost of fencing per 10 m = ₹ 700

Cost of fencing 200 m = ₹ 700 × 1/10 × 200 = ₹ 14000.

∴ The cost of fencing the square park is ₹ 14000.

Example 2:

Find the smallest number that must be divided from 12500 to make it a perfect square. Also, find the square root of the perfect square number.

Solution:

Prime factorisation of 12500 = 2 × 2 × 5 × 5 × 5 × 5 × 5

On pairing, one 5 is left out. Hence 5 must be divided from 12500 to make it a perfect square.

∴ 12500 ÷ 5 = 2500.

Square root of 2500 = √2500 = 50.

Example 3:

In a garden, mango saplings were planted row-wise such that the number of plants in each row is equal to the number of rows. If a total of 2500 saplings were planted, find the total number of rows.

Solution:

Let there be x number of rows. Since the number of plants in each row is equal to the number of rows.

Number plants in each row = x

Total number of plants = x² = 2500

⇒ x = √2500 = 50

∴ there are 50 rows of mango plants.