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

• 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.

The square root of 252 is a non-terminating and non-repeating 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.

Square Root of 252 Using Prime Factorization Method

• The prime factorization of 252: 2² × 3² × 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

• Square root of 25
• Square root of 22
• Square root of 52
• Square root of 256
• Square root of 49

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.

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.