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Last updated on May 26th, 2025

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Square Root of 3/2

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If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The concept of square roots is applied in various fields, such as engineering, finance, and physics. Here, we will discuss the square root of 3/2.

Square Root of 3/2 for US Students
Professor Greenline from BrightChamps

What is the Square Root of 3/2?

The square root is the inverse operation of squaring a number. The number 3/2 is not a perfect square. The square root of 3/2 is expressed in both radical and exponential form. In radical form, it is expressed as √(3/2), whereas (3/2)^(1/2) in exponential form. √(3/2) is an irrational number because it cannot be expressed as a simple fraction of two integers.

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Finding the Square Root of 3/2

For non-perfect square numbers, the prime factorization method is not applicable. Instead, methods like the long-division method and approximation method are used. Let us explore these methods:

 

  • Long division method
  • Approximation method
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Square Root of 3/2 by Long Division Method

The long division method is useful for finding the square roots of non-perfect square numbers. Here is how we can calculate the square root of 3/2 using this method:

 

Step 1: Convert the fraction 3/2 to a decimal, which is 1.5.

 

Step 2: Use the long division method to find the square root of 1.5.

 

Step 3: Group the digits of 1.5, considering it as 150 in the long division format.

 

Step 4: Find the largest number whose square is less than or equal to 150.

 

Step 5: Continue the long division process until you reach the desired level of precision.

 

The square root of 1.5 is approximately 1.2247, so √(3/2) ≈ 1.2247.

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Square Root of 3/2 by Approximation Method

The approximation method is another approach to finding square roots. This method is relatively easy for estimating the square root of a number. Here is how we can find the square root of 3/2 using approximation:

 

Step 1: Convert the fraction 3/2 to a decimal, which is 1.5.

 

Step 2: Identify two perfect squares between which 1.5 falls. The perfect squares are 1 (1^2) and 4 (2^2), so √1.5 is between 1 and 2.

 

Step 3: Use interpolation to estimate √1.5. The difference between 1.5 and 1 is 0.5, and the difference between 4 and 1 is 3.

 

Step 4: Calculate the approximate value using interpolation: (1.5 - 1) / (4 - 1) = 0.5 / 3 = 0.1667.

 

Step 5: Add this value to the lower bound of 1 to estimate √1.5 ≈ 1.1667. For more precision, further calculations can be done.

 

The square root of 3/2 is approximately 1.2247.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 3/2

Students often make errors when calculating square roots, such as neglecting the negative square root or incorrect usage of methods. Let us examine some common mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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Students should remember that numbers have both positive and negative square roots. However, in many practical applications, only the positive square root is used.

For example: √(3/2) ≈ ±1.2247, but we usually consider the positive value.

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Square Root of 3/2 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 if its side length is given as √(3/2)?

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The area of the square is approximately 1.5 square units.

Explanation

The area of a square = side².

The side length is given as √(3/2).

Area of the square = (√(3/2))² = 3/2 ≈ 1.5

Therefore, the area of the square is 1.5 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A rectangle has an area of 3/2 square units. If one side is √(3/2), what will be the length of the other side?

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The other side is 1 unit.

Explanation

Area = length × width.

Given the area is 3/2 and one side is √(3/2), the other side is calculated as (3/2) / √(3/2) = 1.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(3/2) × 4.

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The result is approximately 4.898.

Explanation

First, find the square root of 3/2, which is approximately 1.2247.

Then multiply 1.2247 by 4: 1.2247 × 4 ≈ 4.898.

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Max, the Girl Character from BrightChamps

Problem 4

What is the square root of (1.5 + 0.5)?

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The square root is approximately 1.414.

Explanation

First, calculate the sum: 1.5 + 0.5 = 2.

Then find the square root of 2, which is approximately 1.414.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length is √(3/2) units and the width is 2 units.

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The perimeter of the rectangle is approximately 6.4494 units.

Explanation

Perimeter of a rectangle = 2 × (length + width). Perimeter = 2 × (√(3/2) + 2) ≈ 2 × (1.2247 + 2) ≈ 6.4494 units.

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FAQ on Square Root of 3/2

1.What is √(3/2) in its simplest form?

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2.Is 3/2 a perfect square?

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3.Calculate the square of 3/2.

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4.Is 3/2 a rational number?

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5.What is the decimal representation of 3/2?

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

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 3/2?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 3/2?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 3/2

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: The square root of 4 is 2, because 2 × 2 = 4.

 

  • Irrational number: An irrational number cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating. Example: √2 is irrational.

 

  • Rational number: A rational number can be expressed as a fraction with an integer numerator and a non-zero integer denominator. Example: 3/2 is rational.

 

  • Decimal: A decimal represents a non-integer number using place value and a decimal point. Example: 1.5 is a decimal representation of 3/2.

 

  • Interpolation: Interpolation is a method of estimating unknown values that fall between known values. It is used in approximating square roots, like estimating √1.5.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of 3/2, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting part of every child’s math adventure!
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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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