Square Root of 252
The square root of 252 defines a number whose square results in the initial given number 252. As 252 is not a perfect square, hence, it is difficult to express 252 in terms of two same numbers. Hence, the square root of 252 results in an irrational number Let’s solve for the value of the square root of 252 using few different methods and solve some interesting problems as well.
 Square root of 252: √252 = 15.874507
 Square of 252: (252)^{2 }= 63504
1.  What Is the Square Root of 252? 
2.  Is Square Root of 252 Rational or Irrational? 
3.  How to Find the Square Root of 252? 
4.  Important Notes on Square Root of 252 
5.  FAQs on Square Root of 252 
What is The Square Root of 252?
 The square root of 252 in decimal form is = 15.874507.
 The square root of 252 can be written as √252 and (252)^{1/2}.
 The square root of 252 can be simplified to 6√7.
 The number 252 is not a perfect square as its square root is not an integer.
Is Square Root of 252 Rational or Irrational?
The square root of 252 is a nonterminating and nonrepeating number. Hence, the square root of 252 is an irrational number because it cannot be expressed in the form of p/q where q ≠ 0.
How to Find the Square root of 252?
Square Root of 252 Using Prime Factorization Method
 The prime factorization of 252: 2^{2} × 3^{2} × 7.
 The prime factors of 252 in pairs: (2 × 2) × (3 × 3) × 7.
 Now, the square root of 252: √252 = √((2 × 2) × (3 × 3) × 7).
 So, the square root of 252 = (2 × 3)√7 = 6√7.
Square Root of 252 By Long Division
 Start grouping the digits by drawing a line above that from the unit’s place in pairs of two. We get two pairs in this case (2 & 52).
 Find a number(b) whose product with itself b × b ≤ 2. So, b will be 1 as 1 × 1 ≤ 1.
 We get the quotient and remainder as 1. Now, add the divisor b with itself. Thus, we get the new divisor 2.
 Bring down the next pair of 52. So, our new dividend is 152. Now find a number(m) such that 2m × m ≤ 152. The number m will be 5 as 25 × 5 = 125 ≤ 160. Thus, thus we get the remainder as 4.
 Add a decimal in the dividend and quotient part simultaneously. Also, add 3 pairs of zero in the dividend part (252. 00 00 00) and repeat the above step for all the pairs of zero.
So, we get the square root of √252 = 15.874 by the long division method.
Explore square roots using illustrations and interactive examples
Important Notes:
 The number 252 is not a perfect square.
 The square root of 252 is an irrational number.
 The square root of 252 is an imaginary number.
Square Root of 252 Solved Examples

Example 1: Mario wants to find out the square root of 252. Can you help Mario?
Solution:
The square root of negative numbers is imaginary numbers because a square of any number (positive or negative) will result in a positive number. So, the square of 252 is written as √252 = ±15.8745i. (where i = √1). 
Example 2: Find the square root of 252 using the approximation method?
Solution:
 First, find two consecutive perfect squares between which the number 252 will lie. The two perfect squares are 225 (152) and 256 (162). Therefore, the whole number part of the square root of 252 will be 15.
 Now, for the decimal part, we will use the below formula:
 (Given number  smaller perfect square) / (Greater perfect square  smaller perfect square) = (252  225)/(256  225) = 27/31 = 0.87
Hence, the square root of 252 via the approximation method is 15.87.
FAQs on Square Roots of 252
What is the negative square root of 252?
The negative square root of 252 will be 15.8745
What is the square of 252?
The square of 252 is (252)^{2} = 63504
Is the square root of 252 is a rational number?
No, the square root of 252 is not a rational number because we can’t represent it in the form of p/q where q ≠ 0.
Can we find the square root of 252 using the repeated subtraction method?
No, we can’t find the square root of 252 using the repeated subtraction method because the number 252 is not a perfect square.
How is the square root of 252 is expressed in exponential and radical form?
 The square root of 252 is represented as (252)^{1/2} in exponential form.
 The square root of 252 is represented as √252 in radical form.
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