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Square Root of 32 Explained with Simplification

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How to Find the Square Root of 32 in Radical and Decimal Form

The concept of Metric Length is a foundational part of measurement in school maths, science, and daily life. Understanding metric length helps students solve problems in geometry, physics, and competitive exams like JEE, NEET, and Olympiads. Let’s explore the metric system’s units, conversions, and real-world significance.


What is Metric Length?

Metric length refers to measuring distance or size using the metric system, which is used worldwide and is based on units like the meter (m). The metric system is decimal-based, making calculations and conversions simple. Common units include millimeter (mm), centimeter (cm), meter (m), and kilometer (km).


For example, the thickness of a credit card is about 1 mm, your finger is roughly 1 cm wide, a guitar might be 1 m in length, and the distance between two cities is measured in km.


Metric System Table and Conversions

Understanding the conversion between different metric units is easy because each unit is either 10 times larger or smaller than the next. Here’s how the hierarchy looks:


Unit Symbol How Many Meters? Example
Kilometer km 1,000 m Between cities
Hectometer hm 100 m Smallest stadiums
Decameter dam 10 m Swimming pool
Meter (Base Unit) m 1 m Door height
Decimeter dm 0.1 m Fruit width
Centimeter cm 0.01 m Fingernail
Millimeter mm 0.001 m Paper thickness

Each step up or down involves multiplying or dividing by 10.


Metric Length Conversion Tricks

A helpful mnemonic for remembering the order is: King Henry Died Drinking Chocolate Milk - Kilo, Hecto, Deca, (Meter), Deci, Centi, Milli.

  • To convert larger to smaller units: Multiply (e.g., m to mm: multiply by 1000)
  • To convert smaller to larger units: Divide (e.g., mm to m: divide by 1000)

For example:

  • 1 km = 1,000 m
  • 1 m = 100 cm
  • 1 cm = 10 mm
  • 1 m = 1,000 mm

The SI unit of length is the meter (m).


Key Metric Length Formulae

  • To convert km to m: Multiply km by 1,000
  • To convert m to cm: Multiply m by 100
  • To convert cm to mm: Multiply cm by 10
  • To convert mm to m: Divide mm by 1,000

Example: To convert 5.7 meters to centimeters: 5.7 × 100 = 570 cm.


Worked Examples: Metric Length Conversion

Example 1: Kilometers to Meters

Convert 3.2 kilometers to meters.

  1. 1 km = 1,000 meters
  2. So, 3.2 km × 1,000 = 3,200 meters

Example 2: Centimeters to Meters

Convert 250 cm to meters.

  1. 1 m = 100 cm, so divide by 100
  2. 250 cm ÷ 100 = 2.5 meters

Example 3: Millimeters to Centimeters

Convert 75 mm to cm.

  1. 1 cm = 10 mm
  2. 75 mm ÷ 10 = 7.5 cm

Practice Problems

  • Convert 8 km to meters.
  • Change 630 mm into centimeters.
  • A table is 1.2 m long. What is its length in cm?
  • Convert 0.75 meters to millimeters.
  • How many centimeters are there in 2.5 meters?

Common Mistakes to Avoid

  • Confusing conversion directions (e.g., multiplying instead of dividing, or vice versa).
  • Misplacing the decimal point when converting between units.
  • Forgetting that 1 m = 100 cm (not 1,000 cm).
  • Not labeling answers with correct units (always include units!).

Real-World Applications of Metric Length

Metric length is used daily—measuring classroom objects, tracking running distances, making science experiments, or comparing rainfall. Standard international sports fields, city maps, fabric stores, and even mobile phone screens are measured in meters, centimeters, or millimeters. Learning metric length prepares you for both academics and daily tasks!

At Vedantu, we help students master metric units and conversions with interactive examples and practice so you can confidently solve any measurement problem.

For more on related topics, check out our guides on the Number System, Simplifying Fractions, and Area of a Triangle on Vedantu.


In this topic, we learned about Metric Length—understanding units, conversions, formulas, and applications. Mastering these basics is important for exams and for measuring anything in daily life, ensuring your knowledge is practical and future-ready.


FAQs on Square Root of 32 Explained with Simplification

1. What is the square root of 32?

The square root of 32 is √32 = 4√2 ≈ 5.657.

  • 32 can be written as 16 × 2.
  • √32 = √(16 × 2) = √16 × √2.
  • √16 = 4, so √32 = 4√2.
  • In decimal form, √32 ≈ 5.657.
This is the simplified radical and approximate decimal form of the square root of 32.

2. How do you simplify the square root of 32?

To simplify √32, factor it into perfect squares and multiply outside the radical to get 4√2.

  • Step 1: Factor 32 = 16 × 2.
  • Step 2: Apply √(a × b) = √a × √b.
  • Step 3: √32 = √16 × √2.
  • Step 4: √16 = 4, so the simplified form is 4√2.
This method is called simplifying a radical using prime factorization or perfect square factors.

3. Is the square root of 32 a rational number?

The square root of 32 is an irrational number because it cannot be written as a simple fraction.

  • √32 = 4√2.
  • Since √2 is irrational, multiplying it by 4 keeps it irrational.
  • Its decimal form, ≈ 5.657…, is non-terminating and non-repeating.
Therefore, √32 is irrational.

4. What is the exact value of √32?

The exact value of √32 is 4√2.

  • Exact value means writing the answer in radical form.
  • 32 = 16 × 2.
  • √32 = √16 × √2 = 4√2.
The decimal 5.657 is only an approximation, not the exact value.

5. What is the decimal value of the square root of 32?

The decimal value of √32 is approximately 5.657.

  • Use a calculator to evaluate √32.
  • Rounded to three decimal places, √32 ≈ 5.657.
  • It continues infinitely without repeating.
This is the approximate square root of 32 in decimal form.

6. How do you find the square root of 32 using prime factorization?

Using prime factorization, √32 simplifies to 4√2.

  • Step 1: Prime factorize 32 = 2 × 2 × 2 × 2 × 2.
  • Step 2: Pair equal factors: (2 × 2) and (2 × 2), with one 2 left.
  • Step 3: Take one factor from each pair outside the square root.
  • Step 4: √32 = 4√2.
This method groups identical prime factors to simplify radicals.

7. What is √32 in simplest radical form?

The simplest radical form of √32 is 4√2.

  • Find the largest perfect square factor of 32, which is 16.
  • Rewrite 32 as 16 × 2.
  • Simplify: √32 = √16 × √2 = 4√2.
This is called expressing a square root in simplest radical form.

8. Between which two integers does √32 lie?

The square root of 32 lies between 5 and 6.

  • 5² = 25.
  • 6² = 36.
  • Since 32 is between 25 and 36, √32 is between 5 and 6.
  • More precisely, √32 ≈ 5.657.
This helps estimate square roots without a calculator.

9. Is 32 a perfect square?

No, 32 is not a perfect square because it does not have an integer square root.

  • A perfect square has a whole number square root.
  • √32 = 4√2, which is not an integer.
  • Nearby perfect squares are 25 (5²) and 36 (6²).
Therefore, 32 is not a perfect square number.

10. What is the square of 4√2?

The square of 4√2 is 32.

  • (4√2)² = 4² × (√2)².
  • 4² = 16 and (√2)² = 2.
  • 16 × 2 = 32.
This confirms that 4√2 is the simplified square root of 32.