Square Root of 3125
The square root of 3125 is expressed as √3125 in the radical form and as (3125)^{½} or (3125)^{0.5} in the exponent form. The square root of 3125 rounded up to 9 decimal places is 55.901699437. It is the positive solution of the equation x^{2} = 3125. We can express the square root of 3125 in its lowest radical form as 25 √5.
 Square Root of 3125: 55.90169943749474
 Square Root of 3125 in exponential form: (3125)^{½} or (3125)^{0.5}
 Square Root of 3125 in radical form: √3125 or 25 √5
1.  What is the Square Root of 3125? 
2.  How to find the Square Root of 3125? 
3.  Is the Square Root of 3125 Irrational? 
4.  FAQs 
What is the Square Root of 3125?
The square root of 3125, (or root 3125), is the number which when multiplied by itself gives the product as 3125. Therefore, the square root of 3125 = √3125 = 25 √5 = 55.90169943749474.
☛ Check: Square Root Calculator
How to Find Square Root of 3125?
Value of √3125 by Long Division Method
Explanation:
 Forming pairs: 31 and 25
 Find a number Y (5) such that whose square is <= 31. Now divide 31 by 5 with quotient as 5.
 Bring down the next pair 25, to the right of the remainder 6. The new dividend is now 625.
 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 5) such that 10Z × Z <= 625. After finding Z, together 10 and Z (5) form a new divisor 105 for the new dividend 625.
 Divide 625 by 105 with the quotient as 5, giving the remainder = 625  105 × 5 = 625  525 = 100.
 Now, let's find the decimal places after the quotient 55.
 Bring down 00 to the right of this remainder 100. The new dividend is now 10000.
 Add the last digit of quotient to divisor i.e. 5 + 105 = 110. To the right of 110, find a digit Z (which is 9) such that 110Z × Z <= 10000. Together they form a new divisor (1109) for the new dividend (10000).
 Divide 10000 by 1109 with the quotient as 9, giving the remainder = 10000  1109 × 9 = 10000  9981 = 19.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 3125.
Therefore, the square root of 3125 by long division method is 55.9 approximately.
Is Square Root of 3125 Irrational?
The actual value of √3125 is undetermined. The value of √3125 up to 25 decimal places is 55.90169943749474241022934. Hence, the square root of 3125 is an irrational number.
☛ Also Check:
 Square Root of 10  √10 = 3.16228
 Square Root of 37  √37 = 6.08276
 Square Root of 42  √42 = 6.48074
 Square Root of 105  √105 = 10.24695
 Square Root of 200  √200 = 14.14214
 Square Root of 841  √841 = 29
 Square Root of 100  √100 = 10
Square Root of 3125 Solved Examples

Example 1: Solve the equation x^{2} − 3125 = 0
Solution:
x^{2}  3125 = 0 i.e. x^{2} = 3125
x = ±√3125
Since the value of the square root of 3125 is 55.902,
⇒ x = +√3125 or √3125 = 55.902 or 55.902. 
Example 2: If the area of an equilateral triangle is 3125√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} = 3125√3 in^{2}
⇒ a = ±√12500 in
Since length can't be negative,
⇒ a = √12500 = 2 √3125
We know that the square root of 3125 is 55.902.
⇒ a = 111.803 in 
Example 3: If the area of a circle is 3125π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 3125π in^{2}
⇒ r = ±√3125 in
Since radius can't be negative,
⇒ r = √3125
The square root of 3125 is 55.902.
⇒ r = 55.902 in
FAQs on the Square Root of 3125
What is the Value of the Square Root of 3125?
The square root of 3125 is 55.90169.
Why is the Square Root of 3125 an Irrational Number?
Upon prime factorizing 3125 i.e. 5^{5}, 5 is in odd power. Therefore, the square root of 3125 is irrational.
Is the number 3125 a Perfect Square?
The prime factorization of 3125 = 5^{5}. Here, the prime factor 5 is not in the pair. Therefore, 3125 is not a perfect square.
What is the Square Root of 3125?
The square root of 3125 is an imaginary number. It can be written as √3125 = √1 × √3125 = i √3125 = 55.901i
where i = √1 and it is called the imaginary unit.
What is the Square Root of 3125 in Simplest Radical Form?
We need to express 3125 as the product of its prime factors i.e. 3125 = 5 × 5 × 5 × 5 × 5. Therefore, √3125 = √5 × 5 × 5 × 5 × 5 = 25 √5. Thus, the square root of 3125 in the lowest radical form is 25 √5.
What is the Value of 12 square root 3125?
The square root of 3125 is 55.902. Therefore, 12 √3125 = 12 × 55.902 = 670.820.