Square Root of 3/2
2026-02-28 06:02 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3/2

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Last updated on August 5, 2025

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.

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.

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

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.

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.

Problem 1

Can you help Max find the area of a square if its side length is given as √(3/2)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(3/2) × 4.

Okay, lets begin

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.

Well explained 👍

Problem 4

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

Okay, lets begin

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.

Well explained 👍

Problem 5

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

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 3/2

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

2.Is 3/2 a perfect square?

No, 3/2 is not a perfect square because there is no integer that, when squared, equals 3/2.

3.Calculate the square of 3/2.

The square of 3/2 is (3/2)² = 9/4 or 2.25.

4.Is 3/2 a rational number?

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

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.

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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.

Fun Fact

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