115 LearnersLast updated on May 26th, 2025
Square Root of 134
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as mathematics, engineering, and physics. Here, we will discuss the square root of 134.
What is the Square Root of 134?
The square root is the inverse of the square of the number. 134 is not a perfect square. The square root of 134 is expressed in both radical and exponential form. In the radical form, it is expressed as √134, whereas (134)(1/2) is the exponential form. √134 ≈ 11.57584, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 134
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 134, we use the long-division method and approximation method. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 134 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now, let us look at how 134 is broken down into its prime factors.
Step 1: Finding the prime factors of 134 Breaking it down, we get 2 x 67: 21 x 671
Step 2: Now we found out the prime factors of 134. Since 134 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √134 using prime factorization is not possible.
Square Root of 134 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 134, we need to group it as 34 and 1.
Step 2: Now we need to find n whose square is less than or equal to 1. We can say n is ‘1’ because 1 x 1 is less than or equal to 1. Now the quotient is 1, and after subtracting 1-1, the remainder is 0.
Step 3: Now let us bring down 34, which is the new dividend. Add the old divisor with the same number, 1 + 1, we get 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 34. Let us consider n as 1, then 21 x 1 = 21.
Step 6: Subtract 34 from 21; the difference is 13, and the quotient is 11.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1300.
Step 8: Now we need to find the new divisor that is 115 because 2315 x 5 = 11575, which is closest to 13000.
Step 9: Subtracting 11575 from 13000, we get the result 1425.
Step 10: Now the quotient is 11.57.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.
So the square root of √134 is approximately 11.575.
Square Root of 134 by Approximation Method
The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 134 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √134. The smallest perfect square less than 134 is 121 and the largest perfect square greater than 134 is 144. √134 falls somewhere between 11 and 12.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (134 - 121) ÷ (144 - 121) = 0.565 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 11 + 0.565 = 11.565.
Thus, the square root of 134 is approximately 11.565.
Common Mistakes and How to Avoid Them in the Square Root of 134
Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods. Now, let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root as it is the required one.
For example, √50 ≈ 7.071, but there is also -7.071, which should not be forgotten.
Square Root of 134 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √134?
The area of the square is approximately 134 square units.
Explanation
The area of the square = side^2.
The side length is given as √134.
Area of the square = side^2
= √134 x √134
= 134.
Therefore, the area of the square box is approximately 134 square units.
Problem 2
A square-shaped building measuring 134 square feet is built; if each of the sides is √134, what will be the square feet of half of the building?
67 square feet
Explanation
We can just divide the given area by 2 since the building is square-shaped.
Dividing 134 by 2, we get 67.
So half of the building measures 67 square feet.
Problem 3
Calculate √134 x 5.
Approximately 57.88
Explanation
The first step is to find the square root of 134, which is approximately 11.57584.
The second step is to multiply 11.57584 with 5.
So, 11.57584 x 5 = approximately 57.88.
Problem 4
What will be the square root of (128 + 6)?
The square root is 12.
Explanation
To find the square root, we need to find the sum of (128 + 6).
128 + 6 = 134, and then √134 ≈ 11.57584.
Therefore, the square root of (128 + 6) is approximately ±11.57584.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √134 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 99.15 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√134 + 38)
≈ 2 × (11.57584 + 38)
≈ 2 × 49.57584
≈ 99.15 units.
FAQ on Square Root of 134
1.What is √134 in its simplest form?
2.Mention the factors of 134.
3.Calculate the square of 134.
4.Is 134 a prime number?
5.134 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 134?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 134?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 134
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the inverse operation is the square root, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that is used in most applications. Therefore, it is also known as the principal square root.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 134 is 2 x 67.
- Long division method: A method used to find the square root of non-perfect square numbers by performing a series of division steps.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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