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849 LearnersLast updated on August 5, 2025
Square Root of 0.9
What is the Square Root of 0.9?
The square root is the inverse operation of squaring a number. Since 0.9 is not a perfect square, its square root is expressed in both radical and exponential form. In radical form, it is expressed as √0.9, whereas in exponential form it is (0.9)^(1/2). √0.9 ≈ 0.94868, which is an irrational number because it cannot be expressed as a simple fraction of two integers.
Finding the Square Root of 0.9
For non-perfect square numbers, methods such as the long division method and approximation method are used. Let us explore these methods:
- Long division method
- Approximation method
Square Root of 0.9 by Long Division Method
The long division method is useful for finding the square roots of numbers that are not perfect squares. Let us learn how to find the square root of 0.9 using this method, step by step:
Step 1: Begin by grouping 0.9 as 0.90.
Step 2: Find 'n' such that n^2 is less than or equal to 0.9. Here, n is 0 as 0^2 = 0.
Step 3: Now bring down 90 as the new dividend. Add the previous divisor (0) with itself to get 0, and double it to get 0.
Step 4: Find the value of n such that 2n*n is less than or equal to 90. Let n be 3, then 2*3*3 = 18.
Step 5: Subtract 18 from 90 to get 72.
Step 6: Add a decimal point to the quotient, making it 0.9, and bring down two zeros to make the new dividend 7200.
Step 7: Use 6 as the next digit of the quotient. Now the divisor is 39, and 396*6 = 2376.
Step 8: Subtracting 2376 from 7200 gives 4824.
Step 9: Continue these steps until sufficiently accurate.
The approximate square root of 0.9 is 0.94868.
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Square Root of 0.9 by Approximation Method
The approximation method is another way of finding square roots. Here's how you can find the square root of 0.9 using this method:
Step 1: Identify the perfect squares closest to 0.9. The closest are 0.81 (which is 0.9^2) and 1 (which is 1.0^2).
Step 2: Since 0.9 is closer to 0.81, the square root of 0.9 is closer to 0.9 than to 1.
Step 3: Use interpolation or a calculator for a precise value: √0.9 ≈ 0.94868.
Common Mistakes and How to Avoid Them in the Square Root of 0.9
Students often make mistakes when finding square roots, such as overlooking negative square roots or skipping steps in the long division method. Let's review some common mistakes and how to avoid them.
Mistake 1
Forgetting about the negative square root
It is important to remember that numbers have both positive and negative square roots. The principal square root, however, is usually the positive one we are interested in.
For example, √0.9 ≈ 0.94868, but -0.94868 is also a square root.
Mistake 2
Not adding the square root symbol in proper places
Incorrectly using the square root symbol is a common error. Simplifying expressions inside the square root is important before moving to the next step.
For example, √(0.5 + 0.4) = √0.9 is correct, not √0.5 + √0.4.
Mistake 3
Not finding the correct value of a non-perfect square
Students need to simplify calculations inside the square root to avoid errors in identifying approximate values.
For example, √0.9 ≈ 1 is incorrect; the correct approximation is √0.9 ≈ 0.94868.
Mistake 4
Confusing the square root symbol with the cube root
Students should learn the difference between square roots and cube roots.
For instance, √0.9 and ∛0.9 are different.
Mistake 5
Making mistakes in long division
The long division method involves several steps, and students might accidentally skip steps, leading to incorrect results. Careful attention is required, especially when subtracting or bringing down numbers.
Square Root of 0.9 Examples
Problem 1
Can you help Anna find the area of a square box if its side length is given as √0.49?
The area of the square is 0.49 square units.
Explanation
The area of the square = side^2.
The side length is given as √0.49.
Area of the square = side^2 = √0.49 x √0.49 = 0.7 x 0.7 = 0.49.
Therefore, the area of the square box is 0.49 square units.
Problem 2
A square-shaped garden measuring 0.9 square meters is built. If each of the sides is √0.9, what will be the square meters of half of the garden?
0.45 square meters
Explanation
For a square-shaped area, half the area is simply half the total area.
Dividing 0.9 by 2 = we get 0.45.
So, half of the garden measures 0.45 square meters.
Problem 3
Calculate √0.9 x 5.
4.7434
Explanation
First, find the square root of 0.9, which is approximately 0.94868, then multiply by 5. 0.94868 x 5 = 4.7434
Problem 4
What will be the square root of (0.81 + 0.09)?
The square root is 1.
Explanation
To find the square root, compute the sum of (0.81 + 0.09), which equals 0.9.
The square root of 0.9 is approximately 0.94868, but √(0.81 + 0.09) = √0.9 ≈ 0.94868.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √0.81 units and the width ‘w’ is 0.5 units.
The perimeter of the rectangle is 2.8 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√0.81 + 0.5) = 2 × (0.9 + 0.5) = 2 × 1.4 = 2.8 units.
FAQ on Square Root of 0.9
1.What is √0.9 in its simplest form?
2.Mention the factors of 0.9.
3.Calculate the square of 0.9.
4.Is 0.9 a prime number?
5.0.9 is divisible by?
Important Glossaries for the Square Root of 0.9
- Square root: A square root is a value that, when multiplied by itself, gives the original number. For example, 0.3^2 = 0.09, so the square root of 0.09 is 0.3.
- Irrational number: An irrational number cannot be written as a simple fraction of two integers. For example, the square root of 0.9 is an irrational number.
- Approximation method: This method is used to find a close estimate of a number's square root, particularly useful for non-perfect squares.
- Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 1 is a perfect square because 1^2 = 1.
- Decimal: A decimal number has a whole number and a fractional part separated by a decimal point, such as 0.9 or 0.94868.
Vikrant Sharma
About the Author
Vikrant Sharma 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.
