Square Root of 3249
The square root of 3249 is expressed as √3249 in the radical form and as (3249)^{½} or (3249)^{0.5} in the exponent form. The square root of 3249 is 57. It is the positive solution of the equation x^{2} = 3249. The number 3249 is a perfect square.
 Square Root of 3249: 57
 Square Root of 3249 in exponential form: (3249)^{½} or (3249)^{0.5}
 Square Root of 3249 in radical form: √3249
1.  What is the Square Root of 3249? 
2.  How to find the Square Root of 3249? 
3.  Is the Square Root of 3249 Rational? 
4.  FAQs 
What is the Square Root of 3249?
The square root of 3249, (or root 3249), is the number which when multiplied by itself gives the product as 3249. Therefore, the square root of 3249 = √3249 = 57.
ā Check: Square Root Calculator
How to Find Square Root of 3249?
Value of √3249 by Long Division Method
Explanation:
 Forming pairs: 32 and 49
 Find a number Y (5) such that whose square is <= 32. Now divide 32 by 5 with quotient as 5.
 Bring down the next pair 49, to the right of the remainder 7. The new dividend is now 749.
 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 7) such that 10Z × Z <= 749. After finding Z, together 10 and Z (7) form a new divisor 107 for the new dividend 749.
 Divide 749 by 107 with the quotient as 7, giving the remainder = 749  107 × 7 = 749  749 = 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 3249 by long division method is 57.
Is Square Root of 3249 Rational?
The value of √3249 is 57. Hence, the square root of 3249 is a rational number.
ā Also Check:
 Square Root of 162  √162 = 12.72792
 Square Root of 90  √90 = 9.48683
 Square Root of 34  √34 = 5.83095
 Square Root of 100  √100 = 10
 Square Root of 288  √288 = 16.97056
 Square Root of 72  √72 = 8.48528
 Square Root of 33  √33 = 5.74456
Square Root of 3249 Solved Examples

Example 1: Solve the equation x^{2} − 3249 = 0
Solution:
x^{2}  3249 = 0 i.e. x^{2} = 3249
x = ±√3249
Since the value of the square root of 3249 is 57,
⇒ x = +√3249 or √3249 = 57 or 57. 
Example 2: If the surface area of a sphere is 12996π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 12996π in^{2}
⇒ r = ±√3249 in
Since radius can't be negative,
⇒ r = √3249
The square root of 3249 is 57.
⇒ r = 57 in 
Example 3: If the area of an equilateral triangle is 3249√3 in^{2}. 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)a^{2} = 3249√3 in^{2}
⇒ a = ±√12996 in
Since length can't be negative,
⇒ a = √12996 = 2 √3249
We know that the square root of 3249 is 57.
⇒ a = 114 in
FAQs on the Square Root of 3249
What is the Value of the Square Root of 3249?
The square root of 3249 is 57.
Why is the Square Root of 3249 a Rational Number?
Upon prime factorizing 3249 i.e. 3^{2} × 19^{2}, we find that all the prime factors are in even power. This implies that the square root of 3249 is a positive integer. Therefore, the square root of 3249 is rational.
If the Square Root of 3249 is 57. Find the Value of the Square Root of 32.49.
Let us represent √32.49 in p/q form i.e. √(3249/100) = 32.49/10 = 5. Hence, the value of √32.49 = 5
What is the Square Root of 3249?
The square root of 3249 is an imaginary number. It can be written as √3249 = √1 × √3249 = i √3249 = 57i
where i = √1 and it is called the imaginary unit.
Is the number 3249 a Perfect Square?
The prime factorization of 3249 = 3^{2} × 19^{2}. Here, all the numbers are in the power of 2. This implies that the square root of 3249 is a positive integer. Therefore, 3249 is a perfect square.
Evaluate 12 plus 4 square root 3249
The given expression is 12 + 4 √3249. We know that the square root of 3249 is 57. Therefore, 12 + 4 √3249 = 12 + 4 × 57 = 12 + 228 = 240