Square Root of 132

The square root of 132 can be a rational or irrational number. The square root of all positive numbers is real while the square root of all negative numbers is imaginary numbers. Now, with the help of a few different approaches, we will calculate the square root of 132 and will solve few interesting problems along the way as well.

• Square root of 132: √132 = 11.4891
• Square of 132: (132)² = 17424

• The square root of 132 in decimal form is 11.4891
• The square root of 132 is written as √132 in radical form
• The square root of 132 is written as (132)^1/2 in exponential form

The square root of 132 is neither an integer nor a terminating/repeating number. Thus, it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the square root of 132 is an irrational number.

We will now calculate the square root of 132 using the below-given methods:

Square Root of 132 Using Approximation Method

• Find consecutive perfect squares among which 132 lies.
  The two consecutive perfect squares are 121 (11²) and 144 (12²).
  So, the whole number part of the square root of 132 is 11
• Now, for the decimal part we will use the below formula:
  (Given number - Smaller perfect square) / (Greater perfect square - smaller perfect square)
  = (132 – 121)/(144 – 121) = 11/23 = 0.478
• So, the approx. value of the square root of 132 by the approximation method is 11.478

Square Root of 132 By Long Division

Now we will calculate the square root of 132 by the long division method.

• Divide the digits from the right side into pairs of two by putting a bar on top of them. In the case of 132, we will have two pairs 32 and 1(pairing from right).
• Now, find a number(t) whose square is ≤ 1. The value of t will be 1 as 1 × 1 = 1≤ 1.
• We get the quotient (1). Now, add the divisor t with itself and get the new divisor 2t (2).
• Drag the next pair (new dividend becomes 032) and find a number (a) such that 2a × a ≤ 32. The value of a comes out to be 1.
• Now, put a decimal after 132 and 11 simultaneously. Also, add 3 pairs of zero in the dividend after the decimal (132.00 00 00) and repeat the above step for the remaining three pairs of zero.

So, we get the value of the square root of √132 = 11.489 by the long division method.

Explore square roots using illustrations and interactive examples

• Square root of 32
• Square root of 13
• Square root of 135
• Square root of 130
• Square root of 136

• The square root of 132 is an irrational number.
• The number 132 is not a perfect square.
• The square root of -132 is an imaginary number.

What is the negative square root of 132?

The negative square root of 132 is -11.489.

What is the square of 132?

The square of 132 is (132)² = 17424.

What is the prime factorization of 132?

The prime factorization of 132 is: 2² × 3 × 11

Is the square root of 132 rational?

No, the square root of 132 is not a rational number.
Because the square root of 132 is a non-terminating and non-repeating number thus, cannot be expressed in the form of p/q where q≠ 0.

Can we calculate the square root of 132 using the repeated subtraction method?

No, we cannot find the square root of 132 using the repeated subtraction method.
Because the number 132 is not a perfect square.