Last updated on May 26th, 2025
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.
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.
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
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.
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.
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.
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.
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.
The side length is the square root of the area: s = √(7/8).
Calculating gives: s ≈ 0.935414 meters.
Calculate 5 times the square root of 7/8.
Approximately 4.67707
First, find the square root of 7/8, which is approximately 0.935414. Then multiply by 5: 5 × 0.935414 = 4.67707.
What is the square root of the sum of 7/8 and 1/8?
The square root is 1.
First, find the sum: 7/8 + 1/8 = 1. The square root of 1 is 1.
Find the perimeter of a square if its area is 7/8 square units.
Approximately 3.741656 units.
First, find the side: s = √(7/8) ≈ 0.935414.
Then calculate the perimeter: 4 × s ≈ 4 × 0.935414 = 3.741656 units.
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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