Finding Square Roots

P6 Mathematics - Term I, Topic 4

Lesson 3 of 4

Learning Objectives:

• Define and find square roots
• Use the radical symbol (√)
• Understand the relationship between squares and square roots

Quick Review: Squares

• 6² = ?
• 8² = ?
• 9² = ?

Quick Review: Answers

• 6² = 36
• 8² = 64
• 9² = 81

Now let's learn to go BACKWARDS!

The Big Question

If I tell you: ? × ? = 25

And both numbers are the same...

What number did I multiply by itself?

The Answer is 5!

Because 5 × 5 = 25

This is called finding the SQUARE ROOT!

The square root of 25 is 5.

What is a Square Root?

Definition

The square root of a number is the value that, when multiplied by itself, gives that number.

Example:

• What × itself = 25?
• 5 × 5 = 25
• So the square root of 25 is 5

The Square Root Symbol

√ (The Radical Sign)

We write: √25 = 5

Read as: "The square root of 25 equals 5"

Squares and Square Roots: Opposites!

They "undo" each other

Start with 5 → Square → Get 25 → Square root → Back to 5!

Think of it Like This...

Squaring = Going Forward

Square Root = Going Backward

    Square (×itself)
5  ─────────────────→  25
   ←─────────────────
      Square Root (√)

How to Find a Square Root

The Question Method

To find √36, ask yourself:

"What number times ITSELF equals 36?"

• Try: 6 × 6 = 36 ✓
• Answer: √36 = 6

Example 1: √49

What × itself = 49?

Think through your times tables...

• 7 × 7 = 49 ✓

√49 = 7

Example 2: √64

What × itself = 64?

Think through your times tables...

• 8 × 8 = 64 ✓

√64 = 8

Example 3: √100

What × itself = 100?

Think through your times tables...

• 10 × 10 = 100 ✓

√100 = 10

Use Your Squares Table!

Every square has a matching square root!

Square Roots to Memorize

Practice: Find the Square Root

1. √16 = ?
2. √49 = ?
3. √81 = ?
4. √121 = ?

Practice: Answers

1. √16 = 4 (because 4 × 4 = 16)
2. √49 = 7 (because 7 × 7 = 49)
3. √81 = 9 (because 9 × 9 = 81)
4. √121 = 11 (because 11 × 11 = 121)

Complete the Pairs

Fill in the blanks:

1. 4² = , so √ = 4
2. 7² = , so √ = 7
3. 11² = , so √ = 11

Complete the Pairs: Answers

1. 4² = 16, so √16 = 4
2. 7² = 49, so √49 = 7
3. 11² = 121, so √121 = 11

Real-Life Example 1

Square Garden

A square garden has an area of 64 m².
What is the length of one side?

Solution:

• Side × Side = Area
• Side × Side = 64
• √64 = 8 metres

Real-Life Example 2

Square Tiles

A square tile has an area of 81 cm².
What is the side length?

Solution:

• Side = √81
• Side = 9 cm

Real-Life Example 3

Chairs in Rows

49 chairs are arranged in a square formation.
How many chairs are in each row?

Solution:

• Chairs per row = √49
• Chairs per row = 7 chairs

Quick Assessment ✓

1. What is √36?

2. If 8² = 64, what is √64?

3. What does the symbol √ mean?

4. Find √100

Quick Assessment: Answers

1. √36 = 6

2. √64 = 8

3. √ means "square root of" (what × itself equals this number)

4. √100 = 10

The Key Relationship

If n² = m, then √m = n

They are INVERSES!

• 5² = 25, so √25 = 5
• 7² = 49, so √49 = 7

Summary: Square Roots

• Square root finds what number × itself = the given number
• Symbol: √ (radical sign)
• Inverse: Square root "undoes" squaring
• Method: Ask "what × itself = ?"
• Memorize: √1, √4, √9, √16, √25, √36, √49, √64, √81, √100, √121, √144

Homework

1. Find: √4, √25, √49, √100, √144

2. Complete: If n² = 36, then n = ___

3. If n² = 81, then √81 = ___

4. A square playground has area 121 m². Find the side length.

5. Write the relationship between 9² = 81 and √81 = 9

Remember!

Square Root = "What times itself?"

Well Done!

You can now find square roots!

Next lesson: Number Patterns and Sequences

Keep practicing!