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130 LearnersLast updated on December 15, 2025
Square Root of 49/100
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 49/100.
What is the Square Root of 49/100?
The square root is the inverse of the square of the number.
49/100 is a perfect square.
The square root of 49/100 is expressed in both radical and exponential form.
In radical form, it is expressed as √(49/100), whereas (49/100)(1/2) in exponential form. √(49/100) = 7/10, 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 49/100
The prime factorization method is used for perfect square numbers.
For 49/100, we can use the prime factorization method. Let us now learn the following methods:
- Prime factorization method
- Simplification method
Square Root of 49/100 by Prime Factorization Method
The product of prime factors is the prime factorization of a number.
Now let us look at how 49/100 is broken down into its prime factors:
Step 1: Finding the prime factors of 49 and 100 Breaking it down, 49 = 7 x 7 and 100 = 2 x 2 x 5 x 5
Step 2: Now we have found the prime factors of 49 and 100. The second step is to take the square root of each. √49 = √(7 x 7) = 7 √100 = √(2 x 2 x 5 x 5) = 10
Therefore, the square root of 49/100 is 7/10.
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Square Root of 49/100 by Simplification Method
The simplification method makes it easy to find the square roots of fractions. Let us learn how to find the square root of 49/100 using this method:
Step 1: Express each part of the fraction as a square. 49/100 = (72)/(102)
Step 2: Take the square root of the numerator and the denominator. √49/100 = √(72)/√(12) = 7/10
Thus, the square root of 49/100 is 7/10.
Square Root of 49/100 by Approximation Method
The approximation method is not needed for perfect squares like 49/100, as we can directly find the square root by simplification.
However, if desired, an approximation can confirm the result.
Step 1: Recognize that 49/100 is between two perfect squares, 0/100 (0) and 100/100 (1).
Step 2: Calculate the square root, knowing that 49/100 is a perfect square itself.
Thus, 7/10 is an exact result, aligning with our perfect square identification.
Common Mistakes and How to Avoid Them in the Square Root of 49/100
Students often make mistakes while finding the square root, such as confusing perfect squares with non-perfect squares.
Let us look at a few common mistakes and how to avoid them.
Mistake 1
Forgetting that a number can be a perfect square
Students might overlook that fractions like 49/100 can be perfect squares.
Recognizing perfect squares helps simplify calculations.
For example, √(49/100) = 7/10 is often more straightforward than perceived.
Mistake 2
Misplacing the square root symbol
Not using the square root symbol properly can lead to errors.
It is essential to simplify the numbers inside the square root before proceeding.
For example, √(49/100) should be simplified directly to 7/10.
Mistake 3
Overcomplicating calculations for perfect squares
When dealing with perfect squares, students might attempt unnecessary steps.
Recognizing simple cases like √(49/100) = 7/10 can save effort and reduce errors.
Mistake 4
Confusing square roots with cube roots
Students need clarity between square roots and cube roots.
For example, √(49/100) is not the same as โ(49/100). Understanding the distinction prevents errors.
Mistake 5
Incorrectly simplifying fractions before finding square roots
Ensure fractions are simplified correctly before calculating square roots.
Missteps in simplification can lead to incorrect results.
Here, 49/100 is already in simplest form, making √(49/100) straightforward.
Square root of 49/100 Examples
Problem 1
Can you help Emma find the area of a square box if its side length is given as โ(16/25)?
The area of the square is 16/25 square units.
Explanation
The area of the square = side².
The side length is given as √(16/25).
Area of the square = side² = (√16/25) x (√16/25) = 4/5 x 4/5 = 16/25
Therefore, the area of the square box is 16/25 square units.
Problem 2
A square-shaped garden measuring 49/100 square meters is planned; if each of the sides is โ(49/100), what will be the area of half of the garden?
49/200 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 49/100 by 2 = 49/200
So half of the garden measures 49/200 square meters.
Problem 3
Calculate โ(49/100) x 3.
2.1
Explanation
The first step is to find the square root of 49/100, which is 7/10.
The second step is to multiply 7/10 with 3.
So 7/10 x 3 = 21/10 = 2.1
Problem 4
What will be the square root of (49/100 + 9/100)?
The square root is 4/5.
Explanation
To find the square root, we need to find the sum of (49/100 + 9/100).
49/100 + 9/100 = 58/100, and then √(58/100) = √(29/50).
The expression simplifies to 4/5.
Problem 5
Find the perimeter of the rectangle if its length โlโ is โ(49/100) units and the width โwโ is 1 unit.
The perimeter of the rectangle is 2.4 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(49/100) + 1)
= 2 × (0.7 + 1)
= 2 × 1.7
= 3.4 units.
FAQ on Square Root of 49/100
1.What is โ(49/100) in its simplest form?
2.Mention the factors of 49/100.
3.Calculate the square of 49/100.
4.Is 49/100 a rational number?
5.49/100 is divisible by?
Important Glossaries for the Square Root of 49/100
- 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.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Perfect square: A number that is the square of an integer. Example: 49 and 100 are perfect squares.
- Fraction: A way of expressing numbers that are not whole, using two integers, a numerator, and a denominator. Example: 49/100.
- Simplification: The process of reducing a mathematical expression to its simplest form. For example, simplifying √(49/100) to 7/10.
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.
