101 LearnersLast updated on May 26th, 2025
Square Root of 42.25
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 like vehicle design, finance, etc. Here, we will discuss the square root of 42.25.
What is the Square Root of 42.25?
The square root is the inverse of the square of the number. 42.25 is a perfect square. The square root of 42.25 is expressed in both radical and exponential form.
In the radical form, it is expressed as √42.25, whereas (42.25)^(1/2) in exponential form. √42.25 = 6.5, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 42.25
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, methods like long division and approximation are used. Since 42.25 is a perfect square, we can directly calculate its square root.
Square Root of 42.25 by Prime Factorization Method
As 42.25 is a perfect square, we can write it as the square of a rational number. Breaking down 42.25, we have:
Step 1: Write 42.25 as a fraction: 4225/100.
Step 2: The square root of 4225 is 65, and the square root of 100 is 10.
Step 3: Therefore, √42.25 = 65/10 = 6.5. Since 42.25 is already a perfect square, the calculation confirms that the square root is 6.5.
Square Root of 42.25 by Long Division Method
For perfect square numbers like 42.25, the long division method can verify the square root:
Step 1: Start with 42.25 and group the numbers from the decimal point into pairs: 42 | 25.
Step 2: Find a number whose square is closest to 42. This number is 6 because 6 × 6 = 36.
Step 3: Subtract 36 from 42, remainder is 6. Bring down 25 to make it 625.
Step 4: Double the divisor, 6, to get 12. Now, find a digit, n, such that 12n × n is close to 625. n is 5, since 125 × 5 = 625.
Step 5: Subtract 625 from 625 to get 0, confirming the square root is 6.5.
Square Root of 42.25 by Approximation Method
The approximation method can also be used to find the square roots:
Step 1: Identify the perfect squares around 42.25, which are 36 (6^2) and 49 (7^2).
Step 2: Since 42.25 is exactly halfway between 36 and 49, √42.25 is halfway between 6 and 7.
Step 3: Calculate the average: (6 + 7) / 2 = 6.5. Thus, the square root of 42.25 is precisely 6.5.
Common Mistakes and How to Avoid Them in the Square Root of 42.25
Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It's important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root as the primary solution.
For example, √42.25 = 6.5, but there is also -6.5.
Square Root of 42.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √42.25?
The area of the square is 42.25 square units.
Explanation
The area of the square = side^2. The side length is given as √42.25.
Area of the square = side^2 = (√42.25) × (√42.25) = 6.5 × 6.5 = 42.25.
Therefore, the area of the square box is 42.25 square units.
Problem 2
A square-shaped garden measuring 42.25 square meters is built; if each of the sides is √42.25, what will be the square meters of half of the garden?
21.125 square meters
Explanation
Divide the area by 2 as the garden is square-shaped.
Dividing 42.25 by 2 = 21.125.
So half of the garden measures 21.125 square meters.
Problem 3
Calculate √42.25 × 4.
26
Explanation
The first step is to find the square root of 42.25, which is 6.5.
The second step is to multiply 6.5 by 4. So 6.5 × 4 = 26.
Problem 4
What will be the square root of (36 + 6.25)?
The square root is 6.5
Explanation
To find the square root, sum (36 + 6.25). 36 + 6.25 = 42.25, and then √42.25 = 6.5.
Therefore, the square root of (36 + 6.25) is ±6.5.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √42.25 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as 53 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√42.25 + 20) = 2 × (6.5 + 20) = 2 × 26.5 = 53 units.
FAQ on Square Root of 42.25
1.What is √42.25 in its simplest form?
2.Mention the factors of 42.25.
3.Calculate the square of 42.25.
4.Is 42.25 a prime number?
5.42.25 is divisible by?
Important Glossaries for the Square Root of 42.25
- Square root: A square root is the inverse of squaring a number. For example, 6.5^2 = 42.25, and the square root is √42.25 = 6.5.
- Rational number: A rational number can be expressed in the form of p/q, where q is not zero, and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer or rational number. Example: 42.25 is a perfect square because it is 6.5^2.
- Decimal: A decimal is a number that contains a whole number and a fractional part separated by a decimal point, such as 6.5.
- Long division method: A technique used to find the square root of a number, especially for non-perfect squares, involving dividing the number into pairs 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.
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: He loves to play the quiz with kids through algebra to make kids love it.
