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103 LearnersLast updated on March 20th, 2025
Square Root of 89.89
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 89.89
What is the Square Root of 89.89?
The square root is the inverse of the square of the number. 89.89 is not a perfect square. The square root of 89.89 is expressed in both radical and exponential form.
In the radical form, it is expressed as √89.89, whereas (89.89)(1/2) in the exponential form. √89.89 ≈ 9.478, 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 89.89
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 89.89 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 89.89 is broken down into its prime factors.
Step 1: Finding the prime factors of 89.89 Since 89.89 is not a whole number, prime factorization isn't applicable.
Therefore, calculating 89.89 using prime factorization is impossible.
Square Root of 89.89 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 89.89, we need to consider the entire number as a group.
Step 2: Now we need to find n whose square is closest to the whole number part, 89. We can say n as ‘9’ because 9 × 9 = 81 is lesser than or equal to 89. Now the quotient is 9, and after subtracting 81 from 89, the remainder is 8.
Step 3: Bring down the decimal part, 89, which is the new dividend. Add the old divisor with the same number 9 + 9 = 18, which will be our new divisor.
Step 4: The new divisor is now 18n. We need to find the value of n such that 18n × n ≤ 889.
Step 5: Let's consider n as 4, now 184 × 4 = 736.
Step 6: Subtract 736 from 889, the difference is 153, and the quotient is 9.4.
Step 7: Since the dividend is less than the divisor, we need to add more decimal places. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 15300.
Step 8: Now we need to find the new divisor that is 945 because 1895 × 5 = 9475.
Step 9: Subtracting 9475 from 15300, we get the result 5830.
Step 10: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √89.89 is approximately 9.48.
Square Root of 89.89 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 89.89 using the approximation method.
Step 1: Now we have to find the closest perfect square of √89.89. The smallest perfect square less than 89.89 is 81 and the largest perfect square more than 89.89 is 100. √89.89 falls somewhere between 9 and 10.
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 (89.89 - 81) / (100 - 81) = 0.4679.
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 9 + 0.4679, so the square root of 89.89 is approximately 9.47.
Common Mistakes and How to Avoid Them in the Square Root of 89.89
Square root of 89.89 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √89.89?
Explanation
Problem 2
A square-shaped building measuring 89.89 square feet is built; if each of the sides is √89.89, what will be the square feet of half of the building?
Explanation
Problem 3
Calculate √89.89 × 5.
Explanation
Problem 4
What will be the square root of (89 + 0.89)?
Explanation
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √89.89 units and the width ‘w’ is 10 units.
Explanation
FAQ on Square Root of 89.89
1.What is √89.89 in its simplest form?
2.What are the perfect squares around 89.89?
3.Calculate the square of 89.89.
4.Is 89.89 a perfect square?
5.Is 89.89 a prime number?
Important Glossaries for the Square Root of 89.89
- Square root: A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root, that is, √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 has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Decimal approximation: This is the process of finding a number close to the real value of a square root, typically used for non-perfect squares.
- Long division method: A method used to find the square root of non-perfect square numbers using division, allowing for the calculation of decimal places.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
