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Square Root of 2401

The square root of 2401 is expressed as √2401 in the radical form and as (2401)^½ or (2401)^0.5 in the exponent form. The square root of 2401 is 49. It is the positive solution of the equation x² = 2401. The number 2401 is a perfect square.

Square Root of 2401: 49
Square Root of 2401 in exponential form: (2401)^½ or (2401)^0.5
Square Root of 2401 in radical form: √2401

Square Root of 2401

1.	What is the Square Root of 2401?
2.	How to find the Square Root of 2401?
3.	Is the Square Root of 2401 Rational?
4.	FAQs

What is the Square Root of 2401?

The square root of 2401, (or root 2401), is the number which when multiplied by itself gives the product as 2401. Therefore, the square root of 2401 = √2401 = 49.

☛ Check: Square Root Calculator

How to Find Square Root of 2401?

Square Root of 2401 by Long Division Method

Value of √2401 by Long Division Method

Explanation:

Forming pairs: 24 and 01
Find a number Y (4) such that whose square is <= 24. Now divide 24 by 4 with quotient as 4.
Bring down the next pair 01, to the right of the remainder 8. The new dividend is now 801.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 9) such that 8Z × Z <= 801. After finding Z, together 8 and Z (9) form a new divisor 89 for the new dividend 801.
Divide 801 by 89 with the quotient as 9, giving the remainder = 801 - 89 × 9 = 801 - 801 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 2401 by long division method is 49.

Is Square Root of 2401 Rational?

The value of √2401 is 49. Hence, the square root of 2401 is a rational number.

☛ Also Check:

Square Root of 136 - √136 = 11.66190
Square Root of 54 - √54 = 7.34847
Square Root of 100 - √100 = 10
Square Root of 200 - √200 = 14.14214
Square Root of 108 - √108 = 10.39230
Square Root of 116 - √116 = 10.77033
Square Root of 75 - √75 = 8.66025

Square Root of 2401 Solved Examples

Example 1: Solve the equation x² − 2401 = 0

Solution:

x² - 2401 = 0 i.e. x² = 2401
x = ±√2401
Since the value of the square root of 2401 is 49,
⇒ x = +√2401 or -√2401 = 49 or -49.
Example 2: If the surface area of a sphere is 9604π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 9604π in²
⇒ r = ±√2401 in
Since radius can't be negative,
⇒ r = √2401
The square root of 2401 is 49.
⇒ r = 49 in
Example 3: If the area of an equilateral triangle is 2401√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 2401√3 in²
⇒ a = ±√9604 in
Since length can't be negative,
⇒ a = √9604 = 2 √2401
We know that the square root of 2401 is 49.
⇒ a = 98 in

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FAQs on the Square Root of 2401

What is the Value of the Square Root of 2401?

The square root of 2401 is 49.

Why is the Square Root of 2401 a Rational Number?

Upon prime factorizing 2401 i.e. 7⁴, we find that all the prime factors are in even power. This implies that the square root of 2401 is a positive integer. Therefore, the square root of 2401 is rational.

If the Square Root of 2401 is 49. Find the Value of the Square Root of 24.01.

Let us represent √24.01 in p/q form i.e. √(2401/100) = 24.01/10 = 4. Hence, the value of √24.01 = 4

What is the Square Root of -2401?

The square root of -2401 is an imaginary number. It can be written as √-2401 = √-1 × √2401 = i √2401 = 49i
where i = √-1 and it is called the imaginary unit.

Is the number 2401 a Perfect Square?

The prime factorization of 2401 = 7⁴. Here, all the numbers are in the power of 2. This implies that the square root of 2401 is a positive integer. Therefore, 2401 is a perfect square.

What is the Square of the Square Root of 2401?

The square of the square root of 2401 is the number 2401 itself i.e. (√2401)² = (2401)^2/2 = 2401.

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