Square Root of 3025

The square root of 3025 is a number whose square is 3025. If the square root of a number is an integer, then the number is a perfect square number. The Square and square of a number are inverses of each other. If a² = b then √b = a. This article teaches us how to find the square root of 3025 using different methods.

Learn more about square and square roots.

What is Square Root of 3025?

The square root of 3025 is a number which is when multiplied twice by itself, gives the answer 3025. We can also say that the square root of 3025 is the solution of the equation x² – 3025 = 0. As the equation is quadratic, it must have two roots; likewise, whenever we find the square root of any number, we get two roots – positive and negative.

Also read: Properties of square numbers.

<image>

How to Find the Square Root of 3025?

Now, we shall find the square root of 3025 using the prime factorisation and long division method.

Prime Factorisation Method

To find the square root of 3025 by the prime factorisation method, we first prime factorise 3025 and then make pairs of two to get the square root.

Prime factorisation of 3025 = 5 × 5 × 11 × 11

Square root of 3025 = √[5 × 5 × 11 × 11] = 5 × 11.

Long Division Method

To find the square root of 3025 by the long division method, we shall write 3025 as the dividend and pair its digits from right to left. Now, we shall calculate the square root of 3025 as follows:

To learn how to find the square root of any number 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 3025

Example 1:

Find the perimeter of the rectangle whose area is 605 cm² and breadth is one-fifth its length.

Solution:

Let ‘l’ be the length of the rectangle.

The breadth of the rectangle = l/5.

Area of the rectangle = length × breadth = 605 cm²

⇒ l × l/5 = 605

⇒ l² = 605 × 5 = 3025

⇒ l = √3025 = 55 cm

∴ the length of the rectangle = 55 cm

And the breadth of the rectangle = 55/5 = 11 cm.

Perimeter of the rectangle = 2 × (55 + 11) = 132 cm.

Example 2:

Find the roots of the equation (x² + 5)/5 = 606.

Solution:

We have, (x² + 5)/5 = 606

⇒ x² + 5 = 3030

⇒ x² = 3030 – 5

⇒ x = √3025

⇒ x = ± 55

Example 3:

Find the sides of a square whose area is 3025 cm².

Solution:

Let a be the side length of the square.

Area of the square = a² = 3025 cm²

⇒ a = √3025 = 55 (taking positive root as length cannot be negative).

∴ the length of the sides of the square is 55 cm.