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Square Root of 2700

The square root of 2700 is expressed as √2700 in the radical form and as (2700)^½ or (2700)^0.5 in the exponent form. The square root of 2700 rounded up to 10 decimal places is 51.9615242271. It is the positive solution of the equation x² = 2700. We can express the square root of 2700 in its lowest radical form as 30 √3.

Square Root of 2700: 51.96152422706632
Square Root of 2700 in exponential form: (2700)^½ or (2700)^0.5
Square Root of 2700 in radical form: √2700 or 30 √3

Square Root of 2700

1.	What is the Square Root of 2700?
2.	How to find the Square Root of 2700?
3.	Is the Square Root of 2700 Irrational?
4.	FAQs

What is the Square Root of 2700?

The square root of 2700, (or root 2700), is the number which when multiplied by itself gives the product as 2700. Therefore, the square root of 2700 = √2700 = 30 √3 = 51.96152422706632.

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How to Find Square Root of 2700?

Square Root of 2700 by Long Division Method

Value of √2700 by Long Division Method

Explanation:

Forming pairs: 27 and 00
Find a number Y (5) such that whose square is <= 27. Now divide 27 by 5 with quotient as 5.
Bring down the next pair 00, to the right of the remainder 2. The new dividend is now 200.
Add the last digit of the quotient (5) to the divisor (5) i.e. 5 + 5 = 10. To the right of 10, find a digit Z (which is 1) such that 10Z × Z <= 200. After finding Z, together 10 and Z (1) form a new divisor 101 for the new dividend 200.
Divide 200 by 101 with the quotient as 1, giving the remainder = 200 - 101 × 1 = 200 - 101 = 99.
Now, let's find the decimal places after the quotient 51.
Bring down 00 to the right of this remainder 99. The new dividend is now 9900.
Add the last digit of quotient to divisor i.e. 1 + 101 = 102. To the right of 102, find a digit Z (which is 9) such that 102Z × Z <= 9900. Together they form a new divisor (1029) for the new dividend (9900).
Divide 9900 by 1029 with the quotient as 9, giving the remainder = 9900 - 1029 × 9 = 9900 - 9261 = 639.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 2700.

Therefore, the square root of 2700 by long division method is 51.9 approx.

Is Square Root of 2700 Irrational?

The actual value of √2700 is undetermined. The value of √2700 up to 25 decimal places is 51.96152422706631880582339. Hence, the square root of 2700 is an irrational number.

☛ Also Check:

Square Root of 89 - √89 = 9.43398
Square Root of 149 - √149 = 12.20656
Square Root of 106 - √106 = 10.29563
Square Root of 729 - √729 = 27
Square Root of 90 - √90 = 9.48683
Square Root of 40 - √40 = 6.32456
Square Root of 77 - √77 = 8.77496

Square Root of 2700 Solved Examples

Example 1: Solve the equation x² − 2700 = 0

Solution:

x² - 2700 = 0 i.e. x² = 2700
x = ±√2700
Since the value of the square root of 2700 is 51.962,
⇒ x = +√2700 or -√2700 = 51.962 or -51.962.
Example 2: If the area of a circle is 2700π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 2700π in²
⇒ r = ±√2700 in
Since radius can't be negative,
⇒ r = √2700
The square root of 2700 is 51.962.
⇒ r = 51.962 in
Example 3: If the surface area of a sphere is 10800π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 10800π in²
⇒ r = ±√2700 in
Since radius can't be negative,
⇒ r = √2700
The square root of 2700 is 51.962.
⇒ r = 51.962 in

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FAQs on the Square Root of 2700

What is the Value of the Square Root of 2700?

The square root of 2700 is 51.96152.

Why is the Square Root of 2700 an Irrational Number?

Upon prime factorizing 2700 i.e. 2² × 3³ × 5², 3 is in odd power. Therefore, the square root of 2700 is irrational.

If the Square Root of 2700 is 51.962. Find the Value of the Square Root of 27.

Let us represent √27 in p/q form i.e. √(2700/100) = 27/10 = 5.196. Hence, the value of √27.0 = 5.196

What is the Square Root of -2700?

The square root of -2700 is an imaginary number. It can be written as √-2700 = √-1 × √2700 = i √2700 = 51.961i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 2700 in Simplest Radical Form?

We need to express 2700 as the product of its prime factors i.e. 2700 = 2 × 2 × 3 × 3 × 3 × 5 × 5. Therefore, √2700 = √2 × 2 × 3 × 3 × 3 × 5 × 5 = 30 √3. Thus, the square root of 2700 in the lowest radical form is 30 √3.

What is the Value of 1 square root 2700?

The square root of 2700 is 51.962. Therefore, 1 √2700 = 1 × 51.962 = 51.962.

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