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
|1.||What Is the Square Root of 132?|
|2.||Is Square Root of 132 Rational or Irrational?|
|3.||How to Find the Square Root of 132?|
|4.||FAQs on Square Root of 132|
What is the Square Root of 132?
- 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
Is Square Root of 132 Rational or Irrational?
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.
How to Find the Square Root of 132?
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
- 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.
Square Root of 132 Solved Examples
Example 1: By what number 132 should be multiplied to make it a perfect square?
A perfect square is a number whose prime factors are in pairs.
Prime factorization of 132: 22 × 3 × 11 = 22 × 33
Here 33 is not in pair therefore, we will have to multiply it with 33 to make it a perfect square.
132 × 33 = 4356
√4356 = 66.
4356 is a perfect square number.
Example 2: What number should Maria subtract from 132 to obtain a perfect square number? Find the square root of the number.
We know that square root of 132 lies between 11 and 12
Square of 11 is 121
Square of 12 is 144
On subtracting 11 from 132 we get 121. (132 - 11 = 121)
121 is a perfect square number
Hence, the number is 11.
Square root of 11 is 3.3166.
FAQs on Square Roots of 132
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.