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Last updated on May 26th, 2025

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Square Root of 7/2

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If a number is multiplied by itself, the result is a square. The inverse of the square is the square root. The square root has applications in fields like vehicle design, finance, and more. Here, we will discuss the square root of 7/2.

Square Root of 7/2 for Canadian Students
Professor Greenline from BrightChamps

What is the Square Root of 7/2?

The square root is the inverse of the square of a number. 7/2 is not a perfect square. The square root of 7/2 is expressed in both radical and exponential form. In the radical form, it is expressed as √(7/2), whereas in exponential form, it is expressed as (7/2)^(1/2). √(7/2) = 1.8708, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 7/2

We can find the square root of a fraction by finding the square roots of the numerator and the denominator separately. For non-perfect square numbers, approximation methods can be used. Let us now learn the following methods:

 

1. Simplification method

 

2. Approximation method

Professor Greenline from BrightChamps

Square Root of 7/2 by Simplification Method

The simplification method involves finding the square roots of the numerator and the denominator separately.

 

Step 1: Find the square root of the numerator 7. Since 7 is not a perfect square, we approximate √7 ≈ 2.64575.

 

Step 2: Find the square root of the denominator 2. √2 ≈ 1.41421.

 

Step 3: Combine the results: √(7/2) = √7 / √2 ≈ 2.64575 / 1.41421 ≈ 1.8708.

Professor Greenline from BrightChamps

Square Root of 7/2 by Approximation Method

The approximation method is straightforward and involves estimating the square root numerically.

 

Step 1: Estimate √7 ≈ 2.64575 and √2 ≈ 1.41421.

 

Step 2: Divide the estimates: 2.64575 / 1.41421 ≈ 1.8708.

 

Step 3: Therefore, the square root of 7/2 is approximately 1.8708.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 7/2

Students often make mistakes while calculating square roots, such as neglecting the negative square root or mishandling fractions. Let's explore some common mistakes.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. For practical purposes, we often only consider the positive square root.

For example: √(7/2) ≈ ±1.8708, but we typically use the positive value.

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Square Root of 7/2 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √(3.5)?

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The area of the square is 3.5 square units.

Explanation

The area of a square = side^2.

The side length is given as √(3.5).

Area of the square = side^2 = √(3.5) × √(3.5) = 3.5.

Therefore, the area of the square box is 3.5 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A rectangle has an area of 7/2 square feet. If its length is √(7/2), what will be the square feet of half of the rectangle?

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1.75 square feet

Explanation

We can divide the given area by 2 since the area is 7/2 square feet.

Dividing 7/2 by 2 = 7/4 = 1.75

So half of the rectangle measures 1.75 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(7/2) × 10.

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18.708

Explanation

The first step is to find the square root of 7/2, which is approximately 1.8708.

The second step is to multiply 1.8708 by 10.

So 1.8708 × 10 = 18.708.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (7 + 1)?

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The square root is 2.82843.

Explanation

To find the square root, we need to find the sum of (7 + 1). 7 + 1 = 8, and then √8 ≈ 2.82843.

Therefore, the square root of (7 + 1) is ±2.82843.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(7/2) units and the width ‘w’ is 5 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is approximately 13.7416 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√(7/2) + 5) = 2 × (1.8708 + 5) = 2 × 6.8708 = 13.7416 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 7/2

1.What is √(7/2) in its simplest form?

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2.How do you calculate the square root of a fraction?

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3.Calculate the square root of 7/2.

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4.Is 7/2 a rational number?

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5.What are the applications of square roots in real life?

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6.How does learning Algebra help students in Canada make better decisions in daily life?

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7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 7/2?

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8.How do technology and digital tools in Canada support learning Algebra and Square Root of 7/2?

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9.Does learning Algebra support future career opportunities for students in Canada?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 7/2

  • Square root: A square root is the value that, when multiplied by itself, gives the original number. Example: √4 = 2.

 

  • Irrational number: A number that cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating, like √2.

 

  • Fraction: A part of a whole expressed as a ratio of two integers, such as 7/2.

 

  • Approximation: A value or number that is close to the exact amount, often used when an exact value is not needed or is difficult to obtain.

 

  • Division: A mathematical operation where a number is divided into equal parts, often used in finding average values or simplifying expressions.
Professor Greenline from BrightChamps

About BrightChamps in Canada

At BrightChamps, we know algebra is more than just symbols—it’s a key to open many doors! Our aim is to support kids across Canada in grasping important math skills, such as today’s focus on the Square Root of 7/2, highlighting square roots in a fun, engaging, and easy-to-understand way. Whether your child is measuring how fast a roller coaster moves at Canada’s Wonderland, tracking hockey scores, or planning their allowance for the latest gadgets, mastering algebra helps build their confidence for daily tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Canada learn in diverse ways, we tailor lessons to their individual style. From Toronto’s busy streets to British Columbia’s stunning landscapes, BrightChamps brings math to life across Canada. Let’s make square roots a fun part of your child’s math experience!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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