Medium📚 Square Roots

Square Root Example

Grade 8Key Stage 3-4Årskurs 8-9

Problem

Simplify: √72

📝Step-by-Step Solution

Find perfect square factors

Look for the largest perfect square that divides 72. Perfect squares: 1, 4, 9, 16, 25, 36...

Factor 72

72 = 36 × 2. We use 36 because it's the largest perfect square factor of 72.

72 = 36 × 2

Apply the square root property

Use √(ab) = √a × √b to split the radical: √72 = √(36 × 2) = √36 × √2

√72 = √36 × √2

Simplify the perfect square

√36 = 6 (because 6 × 6 = 36)

√36 = 6

Write the final answer

√72 = 6√2

Verify (optional)

(6√2)² = 36 × 2 = 72 ✓

✅Final Answer

6√2

To simplify a square root: (1) Find the largest perfect square factor, (2) Rewrite as product of that perfect square and remaining factor, (3) Take the square root of the perfect square, (4) Leave the non-perfect-square under the radical. Alternative method: Factor into primes: 72 = 2³ × 3² = (2 × 3)² × 2 = 36 × 2.

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