Square Roots by Prime Factorisation

Uganda Primary 7 Mathematics
Topic 3 — Term I

Opening Problem — The Square Garden

A farmer has a square plot with area .

Square Numbers and Perfect Squares to 144

A perfect square equals for some whole number .

The Radical Symbol Means Square Root

The square root is the inverse of squaring.

Rapid fire:

At P7 level, means the positive root only.

Squaring and Square-Rooting Are Inverses

Preview of the method:

The Pairing Method — Four Steps

To find where is a perfect square:

1. Prime factorise
2. Write out each prime factor individually
3. Circle identical pairs of primes
4. Multiply one factor from each pair

Pairing Diagram — Square Root of 900

Worked Example — Square Root of 1764

Worked Example — Square Root of 5929

Division ladder:

Your Turn — Square Root of 441

Find using the pairing method.

Hint: use the division ladder — try dividing by first.

Your Turn — Square Root of 2025

Find using the pairing method.

Hint:

Watch Out! — Multiply, Do Not Add

For :

The selected primes are multiplied, not added.

Watch Out! — Check for a Perfect Square

If the prime factorisation has any odd exponent, the number is not a perfect square.

Example: — the exponent of is odd.

Rule: before applying the method, confirm every exponent is even.

Word Problem — Area of a Square

A square garden has area . Find one side.

Factorise:

Word Problem — Square Arrangement

576 chairs form a square grid. How many chairs per row?

Word Problem — Perimeter from Area

A square room has area . Find its perimeter.

Step 1:

Step 2: Perimeter

Identifying the Operation to Use

A square quantity always leads to a square root.

Watch Out! — Always Verify

After computing , always check by squaring:

Verification is a required step, not optional.

Lesson Summary — The Pairing Method

Four steps:

1. Prime factorise
2. Write factors individually
3. Circle identical pairs
4. Multiply one from each pair

Rules: perfect squares only (all exponents even); multiply, not add; always verify.