Square Root of 2401

The square root of 2401 is equal to 49. It is expressed as √2401 in the radical form and as (2401)^½ in exponential form. Since 49 is a whole number, 2401 is a perfect square. Hence, we can represent 49² = 2401 or √2401 = 49. 2401 is a composite number; hence, we can find its square root value using prime factorisation. In this article, we will learn how to find the square root of 2401 using simple steps.

The square root of 2401 can be represented in two different forms.

What is the Square Root of 2401?

The square root of 2401 is the value that can be multiplied by itself to get the original number. Square root is the reverse method of squaring a number. Thus, if x is a number that is squared to get the value equal to 2401, such that x² = 2401, then, √2401 = x.

So, the square root of 2401 is 49 because the square of 49 is equal to 2401.

√2401 = 49

Note: Square root of 2401 is a rational number because we can represent 49 in the form of P/Q, where Q is not equal to zero.

How to Find the Square Root of 2401?

To find the square root of 2401, we have two methods here:

• Prime Factorisation Method
• Long Division Method

We can find the exact value of √2401 using both methods.

Square Root of 2401 by Prime Factorisation

Prime factorisation of 2401 will result in a product of prime factors. Hence, we have;

2401 = 7 × 7 × 7 × 7

2401 = 7² × 7² [Using exponent law: a^m.aⁿ = a^m+n]

2401 = (7 × 7)² [Using exponent law: a^m.b^m = (a.b)^m]

2401 = (49)²

Now, taking the square root on both the sides, we have;

√2401 = √(49)²

√2401 = 49

Hence, the square root of 2401 is 49.

Square Root of 2401 by Long Division Method

Basically, it is a shortcut method to find the square root of 2401. Follow these steps to find the required square root.

• Step 1: Pair the digits of 2401 such as 24 and 01.
• Step 2: Think of a number that can be multiplied by itself to get a value less than or equal to 24. Thus, 4 is the divisor, such that 4 x 4 = 16.
• Step 3: Subtract 16 from 24 to get 8, and take down the next pair, 01, to make the new dividend equal to 801.
• Step 4: Add 4 to the previous divisor. 4 + 4 = 8. Now, put a digit, say A, next to 8 such that 8A x A is less than or equal to 801. 89 x 9 = 801
• Step 5: Then, divide 801 by 89, taking a quotient equal to 9. So we get, 801 – 801 = 0.
• Step 6: Now that we have got 0 at the end, the further division is not required.

Therefore, the required square root of 2401 is the quotient achieved in the above division method, i.e., √2401 = 49.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

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Solved Examples

Q.1: What is the value of √2401 + √100?

Solution: As we know;

√2401 = 49

√100 = 10

Therefore,

√2401 + √100

⇒ 49 + 10

⇒ 59

Q.2: If the area of a square is 2401 sq. cm, what is the length of the side of the square?

Solution: Given,

Area of square = 2401 sq.cm

Let the length of the side of the square be ‘s’.

According to the area of square formula,

A = s²

2401 = s²

Taking root on both sides, we get;

√2401 = √s²

The square root of 2401 is 49. Therefore,

s = 49

Hence, the length of the side of the square is 49 cm.

Practice Questions

1. Find the value of x if, √2401 – x² = 0.
2. What is the value of √-2401?
3. Evaluate √2401 x 1/49 = ?