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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 x^{2} = 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
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.
☛ Check: Square Root Calculator
How to Find Square Root of 2700?
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.
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 Square Root of 90  √90 = 9.48683
 Square Root of 40  √40 = 6.32456
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Square Root of 2700 Solved Examples

Example 1: Solve the equation x^{2} − 2700 = 0
Solution:
x^{2}  2700 = 0 i.e. x^{2} = 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 in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 2700π in^{2}
⇒ 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 in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 10800π in^{2}
⇒ r = ±√2700 in
Since radius can't be negative,
⇒ r = √2700
The square root of 2700 is 51.962.
⇒ r = 51.962 in
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. 2^{2} × 3^{3} × 5^{2}, 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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