105 LearnersLast updated on May 26th, 2025
Square Root of 7/8
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as engineering, physics, and finance. Here, we will discuss the square root of 7/8.
What is the Square Root of 7/8?
The square root is the inverse of the square of a number. Since 7/8 is a fraction, we express its square root in both radical and exponential form. In the radical form, it is expressed as √(7/8), whereas (7/8)^(1/2) in the exponential form. The square root of 7/8 is approximately 0.935414, which is an irrational number because it cannot be expressed exactly as a fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 7/8
The square root of fractions can be found using various methods such as simplifying the fraction, using the prime factorization for integers, or approximation methods for non-perfect squares. For 7/8, we will consider the following methods: Simplification method Approximation method
Square Root of 7/8 by Simplification Method
To find the square root of a fraction, take the square root of the numerator and the denominator separately:
Step 1: Express 7/8 as a fraction.
Step 2: Find the square roots: √7 and √8.
Step 3: The square root of the fraction is √(7/8) = √7 / √8.
Step 4: Simplify the expression: (√7) / (√8) = (√7 * √2) / (√8 * √2) = √14 / 4.
This process gives us an approximate expression for the square root of 7/8.
Square Root of 7/8 by Approximation Method
The approximation method is useful for finding the square roots of non-perfect squares or fractions. Here's how to approximate the square root of 7/8:
Step 1: Calculate the decimal form of 7/8, which is 0.875.
Step 2: Identify the perfect squares closest to 0.875. The closest perfect squares are 0.81 (which is 0.9^2) and 0.84 (which is 0.916^2).
Step 3: The square root of 0.875 is between 0.9 and 0.916. Using interpolation or a calculator, approximate √0.875 ≈ 0.935414.
Thus, the square root of 7/8 is approximately 0.935414.
Square Root of 7/8 Examples
Problem 1
Can you help Max find the length of the diagonal of a rectangle with sides 7/8 and 3/4?
The diagonal of the rectangle is approximately 1.14 units.
Explanation
The diagonal can be found using the Pythagorean theorem: d = √((7/8)^2 + (3/4)^2).
Calculating gives: d ≈ √(0.765625 + 0.5625)
= √1.328125
≈ 1.14.
Problem 2
A square field has an area of 7/8 square meters. What is the side length of the field?
The side length of the square field is approximately 0.935414 meters.
Explanation
The side length is the square root of the area: s = √(7/8).
Calculating gives: s ≈ 0.935414 meters.
Problem 3
Calculate 5 times the square root of 7/8.
Approximately 4.67707
Explanation
First, find the square root of 7/8, which is approximately 0.935414. Then multiply by 5: 5 × 0.935414 = 4.67707.
Problem 4
What is the square root of the sum of 7/8 and 1/8?
The square root is 1.
Explanation
First, find the sum: 7/8 + 1/8 = 1. The square root of 1 is 1.
Problem 5
Find the perimeter of a square if its area is 7/8 square units.
Approximately 3.741656 units.
Explanation
First, find the side: s = √(7/8) ≈ 0.935414.
Then calculate the perimeter: 4 × s ≈ 4 × 0.935414 = 3.741656 units.
FAQ on Square Root of 7/8
1.What is √(7/8) in its simplest form?
2.Is 7/8 a perfect square?
3.Can 7/8 be expressed as a decimal?
4.Is the square root of 7/8 rational or irrational?
5.How do you approximate the square root of 7/8?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 7/8?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 7/8?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 7/8
- Square root: A square root of a number x is a number y such that y^2 = x. For example, the square root of 16 is 4, because 4^2 = 16.
- Irrational number: An irrational number is a number that cannot be expressed as a fraction p/q, where p and q are integers, and q ≠ 0.
- Fraction: A fraction represents a part of a whole and is expressed as a ratio of two integers, like 7/8.
- Decimal: A decimal is a way of expressing numbers that have a whole number and a fractional part separated by a decimal point, such as 0.875.
- Approximation: An approximation is a value or quantity that is nearly but not exactly correct, used to simplify complex calculations.
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Jaskaran Singh Saluja
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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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