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313 LearnersLast updated on August 5, 2025
Square Root of 4.45
What is the Square Root of 4.45?
The square root is the inverse of squaring a number. 4.45 is not a perfect square. The square root of 4.45 is expressed in both radical and exponential form. In radical form, it is expressed as √4.45, whereas (4.45)^(1/2) in exponential form. √4.45 ≈ 2.11, 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 4.45
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers; instead, long-division and approximation methods are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 4.45 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, group the digits from right to left, including decimals. For 4.45, consider 4.45 as 445.
Step 2: Now, find a number whose square is less than or equal to 4. The number is 2 because 2 × 2 = 4.
Step 3: Subtract 4 from 4, the remainder is 0. Bring down 45.
Step 4: Double the divisor (2), which gives us 4. Now, determine an additional digit for the divisor such that it multiplied by itself is less than or equal to 45.
Step 5: Use 1 as the next digit to form 41. 41 × 1 = 41.
Step 6: Subtract 41 from 45 to get 4.
Step 7: Add decimal points and bring down 00 to get 400. The new divisor becomes 42.
Step 8: Find a digit, say 9, such that 429 × 9 = 3861.
Step 9: Continue the division process until you get the desired accuracy.
So, the square root of √4.45 ≈ 2.11.
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Square Root of 4.45 by Approximation Method
The approximation method is another method for finding 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 4.45 using the approximation method.
Step 1: Find the closest perfect squares to √4.45. The smallest perfect square less than 4.45 is 4, and the largest perfect square greater than 4.45 is 9. √4.45 falls somewhere between 2 and 3.
Step 2: Use linear approximation between 2 and 3. Using the formula (4.45 - 4) / (9 - 4) ≈ 0.09. Now, add this value to the lower bound of the range: 2 + 0.09 = 2.09.
Therefore, √4.45 ≈ 2.11.
Common Mistakes and How to Avoid Them in the Square Root of 4.45
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let us look at a few of those 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 take only the positive square root when dealing with real-world applications.
For example: √50 = 7.07, but there is also -7.07, which should not be overlooked.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that students make. To resolve this, we need to teach students to simplify the numbers inside the square root before proceeding to further steps.
For example: √(12 + 24) ≠ √12 + √24. The correct method is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students is to simplify the numbers inside the square root. This is crucial to avoid mistakes in identifying the approximate value.
For example: √50 ≠ 7; the correct value is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots consistently as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, resulting in a wrong answer. This may happen in the subtraction process or elsewhere in the steps.
Square Root of 4.45 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4.45?
The area of the square is approximately 19.80 square units.
Explanation
The area of a square = side².
The side length is given as √4.45.
Area of the square = side² = (√4.45)² ≈ 2.11 × 2.11 ≈ 4.4521.
Therefore, the area of the square box is approximately 19.80 square units.
Problem 2
A square-shaped building measures 4.45 square meters. If each of the sides is √4.45, what will be the square meters of half of the building?
2.225 square meters
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 4.45 by 2 gives us 2.225.
Half of the building measures approximately 2.225 square meters.
Problem 3
Calculate √4.45 × 5.
Approximately 10.55
Explanation
The first step is to find the square root of 4.45, which is approximately 2.11.
Multiply 2.11 by 5. So, 2.11 × 5 ≈ 10.55.
Problem 4
What will be the square root of (4 + 0.45)?
Approximately 2.11
Explanation
To find the square root, we first compute the sum: 4 + 0.45 = 4.45.
Then, √4.45 ≈ 2.11.
Therefore, the square root of (4 + 0.45) is approximately ±2.11.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4.45 units and the width ‘w’ is 3 units.
The perimeter of the rectangle is approximately 10.22 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4.45 + 3).
Perimeter ≈ 2 × (2.11 + 3) ≈ 2 × 5.11 ≈ 10.22 units.
FAQ on Square Root of 4.45
1.What is √4.45 in its simplest form?
2.What are the factors of 4.45?
3.Calculate the square of 4.45.
4.Is 4.45 a prime number?
5.What is 4.45 divisible by?
Important Glossaries for the Square Root of 4.45
- Square root: A square root is the inverse of squaring a number. For example, 3² = 9, and the inverse is √9 = 3.
- Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers. For example, √2 is irrational.
- Division method: A systematic approach to finding the square root of a number through iterative division steps.
- Decimal: A number that consists of a whole number and a fractional part separated by a decimal point. For example, 7.86.
- Approximation: The process of finding a value close to the actual value, often used when dealing with irrational numbers or non-perfect squares.
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.
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