130 LearnersLast updated on May 26th, 2025
Square Root of 5/8
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 various fields such as vehicle design and finance. Here, we will discuss the square root of 5/8.
What is the Square Root of 5/8?
The square root is the inverse of the square of the number. 5/8 is not a perfect square. The square root of 5/8 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(5/8), whereas (5/8)^(1/2) in the exponential form. √(5/8) is approximately 0.7906, 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 5/8
To find the square root of a fraction, we find the square root of the numerator and the denominator separately. The methods used for non-perfect square numbers include the long-division method and the approximation method. Let us now learn the following methods: - Simplifying the fraction method
- Long division method
- Approximation method
Square Root of 5/8 by Simplifying the Fraction Method
To find the square root of a fraction, take the square root of both the numerator and the denominator separately.
Step 1: The fraction is 5/8.
Step 2: The square root of the numerator 5 is √5, and the square root of the denominator 8 is √8.
Step 3: Therefore, the square root of 5/8 is √5/√8, which can be simplified further by multiplying by √8/√8 to rationalize the denominator, resulting in (√5 * √8) / 8 = √(40)/8 ≈ 0.7906.
Square Root of 5/8 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: Convert 5/8 into decimal form, which is 0.625.
Step 2: Use the long division method to find the square root of 0.625. Begin by pairing the digits from right to left.
Step 3: Find a number whose square is less than or equal to the first pair, 62. In this case, it is 7 because 7*7 = 49, and 8*8 = 64 is too large. The quotient is 7, and the remainder is 13.
Step 4: Bring down the next pair, which is 50, making it 1350. Step 5: Double the quotient and use it as part of the new divisor. Therefore, the new divisor is 140.
Step 6: Find a digit n such that 140n * n is less than or equal to 1350. In this case, n is 9.
Step 7: Subtract 1261 (140*9) from 1350 to get the remainder 89.
Step 8: Continue this process to obtain more decimal places.
The result is approximately 0.7906.
Square Root of 5/8 by Approximation Method
The approximation method is another way to find the square root, and it is easy for estimating the square root of a given number. Let's find the square root of 5/8 using the approximation method.
Step 1: Convert 5/8 to a decimal number, which is 0.625.
Step 2: Identify the perfect squares between which 0.625 falls. It falls between 0.49 (0.7^2) and 0.81 (0.9^2).
Step 3: The square root of 0.625 will thus be between 0.7 and 0.9. Use interpolation or a calculator to find a more accurate value, which is approximately 0.7906.
Common Mistakes and How to Avoid Them in the Square Root of 5/8
Students often make mistakes while finding the square root, such as forgetting about the negative square root or misapplying methods. Let's look at some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically refer to the principal (positive) square root.
For example: √(5/8) ≈ 0.7906, but there is also -0.7906.
Mistake 2
Not simplifying the fraction properly
A common mistake is not simplifying the fraction before finding the square root. Ensure the fraction is in its simplest form before proceeding to find the square root.
Mistake 3
Confusing the square root and cube root symbols
Students need to understand the difference between square root and cube root symbols to avoid confusion.
For example, √(5/8) and ∛(5/8) are different.
Mistake 4
Misapplying the long division method
Finding a square root using the long division method involves several steps. Skipping a step or performing incorrect arithmetic can lead to an incorrect answer.
Mistake 5
Misinterpreting decimal approximations
Mistaking decimal approximations for exact values can lead to errors.
For example, √(5/8) is approximately 0.7906, but it is an irrational number and not exactly equal to 0.7906.
Square Root of 5/8 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(5/8)?
The area of the square is approximately 0.625 square units.
Explanation
The area of the square = side^2.
The side length is given as √(5/8).
Area of the square = (√(5/8))^2
= 5/8
= 0.625 square units.
Therefore, the area of the square box is approximately 0.625 square units.
Problem 2
A square-shaped garden measuring 5/8 square meters is built; if each of the sides is √(5/8), what will be the square meters of half of the garden?
0.3125 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 5/8 by 2 gives 5/16.
Converting to decimal, 5/16 = 0.3125.
So half of the garden measures 0.3125 square meters.
Problem 3
Calculate √(5/8) × 10.
Approximately 7.906
Explanation
The first step is to find the square root of 5/8, which is approximately 0.7906.
The second step is to multiply 0.7906 by 10.
So, 0.7906 × 10 = 7.906.
Problem 4
What will be the square root of (5/8 + 3/8)?
The square root is 1.
Explanation
To find the square root, we need to find the sum of (5/8 + 3/8).
5/8 + 3/8 = 8/8 = 1, and the square root of 1 is ±1.
Therefore, the square root of (5/8 + 3/8) is ±1.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(5/8) units and the width ‘w’ is 1 unit.
We find the perimeter of the rectangle as approximately 3.5812 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(5/8) + 1)
≈ 2 × (0.7906 + 1)
≈ 2 × 1.7906
≈ 3.5812 units.
FAQ on Square Root of 5/8
1.What is √(5/8) in its simplest form?
2.Is 5/8 a perfect square?
3.Calculate the square of 5/8.
4.Is √(5/8) a rational number?
5.What is the decimal approximation of √(5/8)?
Important Glossaries for the Square Root of 5/8
- Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers, where the denominator is not zero.
- Principal square root: The principal square root is the non-negative square root of a number. For example, the principal square root of 9 is 3.
- Rationalizing the denominator: This involves multiplying the numerator and the denominator by a radical that will eliminate the radical in the denominator.
- Fraction: A fraction represents a part of a whole and is composed of a numerator and a denominator, such as 5/8.
Explore More algebra
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.
