103 LearnersLast updated on May 26th, 2025
Square Root of 0.91
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 0.91.
What is the Square Root of 0.91?
The square root is the inverse of the square of a number. 0.91 is not a perfect square. The square root of 0.91 is expressed in both radical and exponential forms. In the radical form, it is expressed as √0.91, whereas (0.91)^(1/2) in the exponential form. √0.91 ≈ 0.9539, 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 0.91
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 and approximation methods are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 0.91 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, pair the numbers starting from the decimal point and moving to the right. For 0.91, we pair as 91.
Step 2: Now, find a number whose square is less than or equal to 91. This number is 9 because 9 x 9 = 81.
Step 3: Now, subtract 81 from 91, giving a remainder of 10. Bring down two zeros to make it 1000.
Step 4: Double the divisor (9) to get 18. We need to find a digit to add to 18 to make a new divisor, which when multiplied by the same digit gives a product less than or equal to 1000.
Step 5: The digit is 5 because 185 x 5 = 925.
Step 6: Subtract 925 from 1000 to get 75. Bring down two more zeros.
Step 7: Continue this process to refine the square root to more decimal places. So the square root of √0.91 ≈ 0.9539.
Square Root of 0.91 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 0.91 using the approximation method.
Step 1: Identify the closest perfect squares to 0.91. The perfect squares are 0.81 (0.9^2) and 1 (1^2).
Step 2: Apply the formula to estimate: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). So, (0.91 - 0.81) / (1 - 0.81) ≈ 0.526. Add this decimal to the smaller square root: 0.9 + 0.0526 ≈ 0.9539. Therefore, the square root of 0.91 is approximately 0.9539.
Common Mistakes and How to Avoid Them in the Square Root of 0.91
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in long division methods. Let's examine a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically consider only the positive square root for practical purposes.
For example, √0.91 ≈ 0.9539, but it also has a negative counterpart, -0.9539.
Square root of 0.91 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.81?
The area of the square is 0.6561 square units.
Explanation
The area of a square = side^2. The side length is given as √0.81. Area of the square = (√0.81)^2 = 0.9 x 0.9 = 0.81. Therefore, the area of the square box is 0.81 square units.
Problem 2
A square-shaped building measuring 0.91 square meters is built; if each of the sides is √0.91, what will be the square meters of half of the building?
0.455 square meters
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 0.91 by 2 = 0.455 So half of the building measures 0.455 square meters.
Problem 3
Calculate √0.91 x 5.
4.7695
Explanation
The first step is to find the square root of 0.91, which is approximately 0.9539.
The second step is to multiply 0.9539 by 5. So, 0.9539 x 5 ≈ 4.7695.
Problem 4
What will be the square root of (0.49 + 0.42)?
The square root is approximately 0.9539.
Explanation
To find the square root, we need to find the sum of (0.49 + 0.42). 0.49 + 0.42 = 0.91, and then √0.91 ≈ 0.9539.
Therefore, the square root of (0.49 + 0.42) is approximately ±0.9539.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √0.81 units and the width ‘w’ is 1 unit.
The perimeter of the rectangle is 3.8 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√0.81 + 1) = 2 × (0.9 + 1) = 2 × 1.9 = 3.8 units.
FAQ on Square Root of 0.91
1.What is √0.91 in its simplest form?
2.How do you find the square root of a non-perfect square?
3.Is 0.91 a perfect square?
4.What is the square of 0.91?
5.Is 0.91 a rational number?
Important Glossaries for the Square Root of 0.91
- Square root: A square root is the inverse of a square. For example, 3^2 = 9, and the inverse of the square is the square root, √9 = 3.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Rational number: A rational number can be expressed as a fraction of two integers, where the denominator is not zero.
- Decimal: A decimal is a number with a whole number and a fractional part separated by a decimal point, such as 7.86.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number into pairs of digits starting from the decimal point.
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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.
