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194 LearnersLast updated on December 15, 2025
Square Root of 49/25
What is the Square Root of 49/25?
The square root is the inverse of the square of the number. 49/25 is a perfect square fraction.
The square root of 49/25 is expressed in both radical and exponential form.
In the radical form, it is expressed as √(49/25), whereas (49/25)(1/2) is the exponential form. √(49/25) = 7/5, 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 49/25
To find the square root of a perfect square fraction, we take the square root of the numerator and the denominator separately.
Let's explore this method:
Square root of the numerator: √49 = 7
Square root of the denominator: √25 = 5
Thus, the square root of 49/25 is 7/5.
Square Root of 49/25 by Prime Factorization Method
The prime factorization method can also be used to find square roots of perfect squares.
Let's see how 49/25 can be broken down:
Step 1: Prime factorization of the numerator and the denominator - 49 = 7 x 7 - 25 = 5 x 5
Step 2: Taking the square root of each part - √49 = 7 - √25 = 5
Therefore, the square root of 49/25 is 7/5.
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Square Root of 49/25 by Long Division Method
The long division method is not needed for perfect square fractions like 49/25, as the square roots of the numerator and the denominator can be easily calculated.
However, if you wish to use this method, you would start by dividing the numerator and denominator separately and finding their square roots:
√49 = 7 using division
√25 = 5 using division
So, the square root of 49/25 is 7/5.
Square Root of 49/25 by Approximation Method
The approximation method is typically used for non-perfect square numbers.
For perfect square fractions, direct calculation is more efficient:
Step 1: Identify perfect square numbers
√49 = 7,
√25 = 5,
Thus, the square root of 49/25 is directly 7/5.
Common Mistakes and How to Avoid Them in the Square Root of 49/25
Students might make mistakes while finding square roots, such as forgetting the properties of fractions or miscalculating individual square roots.
Let us explore some common mistakes in detail.
Mistake 1
Misidentifying Perfect Square Fractions
Students sometimes misidentify fractions as perfect squares.
Remember that a fraction is a perfect square if both its numerator and denominator are perfect squares.
For example, 49/25 is a perfect square because 49 and 25 are perfect squares.
Mistake 2
Ignoring Simplification
Students may forget to simplify fractions after finding square roots.
Ensure the fraction is in its simplest form.
For example, after finding √(49/25) = 7/5, check if 7/5 can be simplified further (it cannot).
Mistake 3
Confusing Numerators and Denominators
Careless mistakes can occur when students mix up numerators and denominators while calculating square roots.
Always keep the numerator and denominator separate.
For example, √(49/25) should be calculated as √49/√25 = 7/5.
Mistake 4
Overcomplicating Simple Calculations
When dealing with perfect squares, students may unnecessarily complicate calculations.
Recognize that √49 = 7 and √25 = 5 are straightforward calculations.
Mistake 5
Confusing Square Root with Reciprocal
Students may mistakenly calculate the reciprocal instead of the square root.
The square root of 49/25 is 7/5, not 5/7.
Square Root of 49/25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(49/25)?
The area of the square is 49/25 square units.
Explanation
The area of the square = side2.
The side length is given as √(49/25).
Area of the square = (√(49/25))2 = (7/5) x (7/5) = 49/25.
Therefore, the area of the square box is 49/25 square units.
Problem 2
A square field has an area of 49/25 square units. What is the side length of the field?
The side length of the field is 7/5 units.
Explanation
If the area of a square is 49/25, then the side length is the square root of 49/25.
√(49/25) = 7/5.
So, the side length of the field is 7/5 units.
Problem 3
Calculate 2 x √(49/25).
2 x √(49/25) = 14/5
Explanation
First, find the square root of 49/25, which is 7/5.
Then, multiply 7/5 by 2.
So, 2 x (7/5) = 14/5.
Problem 4
What is the square root of (49/25) x 25?
The square root is 7.
Explanation
First, simplify (49/25) x 25 = 49.
Then, the square root of 49 is 7.
Therefore, the square root is ±7.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √(49/25) units and the width 'w' is 10 units.
The perimeter of the rectangle is 24 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(49/25) + 10)
= 2 × (7/5 + 10).
Convert 10 to a fraction:
10 = 50/5.
So, Perimeter = 2 × (7/5 + 50/5)
= 2 × (57/5)
= 114/5
= 22.8 units.
FAQ on Square Root of 49/25
1.What is √(49/25) in its simplest form?
2.How do you find the square root of a fraction?
3.Is 49/25 a rational number?
4.What is the decimal form of √(49/25)?
5.Is √(49/25) greater than 1?
Important Glossaries for the Square Root of 49/25
- Square root: A square root is the inverse of a square. For example, if 42 = 16, then the square root of 16 is √16 = 4.
- Rational number: A rational number can be expressed as a fraction p/q, where p and q are integers, and q is not zero.
- Perfect square: A number is a perfect square if it can be expressed as the square of an integer. For example, 49 is a perfect square because it is 72.
- Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.
- Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, such as 1.4.
Vikrant Sharma
About the Author
Vikrant is a passionate Mathematics teacher with over 5 years of teaching experience in both conventional and Vedic Maths. His student-focused approach combines clear concepts with motivation and encouragement, helping students build confidence and develo
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
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