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Square Root of 2400

The square root of 2400 is expressed as √2400 in the radical form and as (2400)^½ or (2400)^0.5 in the exponent form. The square root of 2400 rounded up to 7 decimal places is 48.9897949. It is the positive solution of the equation x² = 2400. We can express the square root of 2400 in its lowest radical form as 20 √6.

Square Root of 2400: 48.98979485566356
Square Root of 2400 in exponential form: (2400)^½ or (2400)^0.5
Square Root of 2400 in radical form: √2400 or 20 √6

Square Root of 2400

1.	What is the Square Root of 2400?
2.	How to find the Square Root of 2400?
3.	Is the Square Root of 2400 Irrational?
4.	FAQs

What is the Square Root of 2400?

The square root of 2400, (or root 2400), is the number which when multiplied by itself gives the product as 2400. Therefore, the square root of 2400 = √2400 = 20 √6 = 48.98979485566356.

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How to Find Square Root of 2400?

Square Root of 2400 by Long Division Method

Value of √2400 by Long Division Method

Explanation:

Forming pairs: 24 and 00
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 00, to the right of the remainder 8. The new dividend is now 800.
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 8) such that 8Z × Z <= 800. After finding Z, together 8 and Z (8) form a new divisor 88 for the new dividend 800.
Divide 800 by 88 with the quotient as 8, giving the remainder = 800 - 88 × 8 = 800 - 704 = 96.
Now, let's find the decimal places after the quotient 48.
Bring down 00 to the right of this remainder 96. The new dividend is now 9600.
Add the last digit of quotient to divisor i.e. 8 + 88 = 96. To the right of 96, find a digit Z (which is 9) such that 96Z × Z <= 9600. Together they form a new divisor (969) for the new dividend (9600).
Divide 9600 by 969 with the quotient as 9, giving the remainder = 9600 - 969 × 9 = 9600 - 8721 = 879.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 2400.

Therefore, the square root of 2400 by long division method is 48.9 approximately.

Is Square Root of 2400 Irrational?

The actual value of √2400 is undetermined. The value of √2400 up to 25 decimal places is 48.98979485566356196394568. Hence, the square root of 2400 is an irrational number.

☛ Also Check:

Square Root of 33 - √33 = 5.74456
Square Root of 120 - √120 = 10.95445
Square Root of 65 - √65 = 8.06226
Square Root of 72 - √72 = 8.48528
Square Root of 256 - √256 = 16
Square Root of 22 - √22 = 4.69042
Square Root of 361 - √361 = 19

Square Root of 2400 Solved Examples

Example 1: Solve the equation x² − 2400 = 0

Solution:

x² - 2400 = 0 i.e. x² = 2400
x = ±√2400
Since the value of the square root of 2400 is 48.990,
⇒ x = +√2400 or -√2400 = 48.990 or -48.990.
Example 2: If the area of a circle is 2400π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 2400π in²
⇒ r = ±√2400 in
Since radius can't be negative,
⇒ r = √2400
The square root of 2400 is 48.990.
⇒ r = 48.990 in
Example 3: If the area of an equilateral triangle is 2400√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 = 2400√3 in²
⇒ a = ±√9600 in
Since length can't be negative,
⇒ a = √9600 = 2 √2400
We know that the square root of 2400 is 48.990.
⇒ a = 97.980 in

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FAQs on the Square Root of 2400

What is the Value of the Square Root of 2400?

The square root of 2400 is 48.98979.

Why is the Square Root of 2400 an Irrational Number?

Upon prime factorizing 2400 i.e. 2⁵ × 3¹ × 5², 2 is in odd power. Therefore, the square root of 2400 is irrational.

What is the Square of the Square Root of 2400?

The square of the square root of 2400 is the number 2400 itself i.e. (√2400)² = (2400)^2/2 = 2400.

What is the Value of 5 square root 2400?

The square root of 2400 is 48.990. Therefore, 5 √2400 = 5 × 48.990 = 244.949.

Evaluate 7 plus 14 square root 2400

The given expression is 7 + 14 √2400. We know that the square root of 2400 is 48.990. Therefore, 7 + 14 √2400 = 7 + 14 × 48.990 = 7 + 685.857 = 692.857

If the Square Root of 2400 is 48.990. Find the Value of the Square Root of 24.

Let us represent √24 in p/q form i.e. √(2400/100) = 24/10 = 4.899. Hence, the value of √24.0 = 4.899

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