Problem
Simplify: √72
📝Step-by-Step Solution
1
Find perfect square factors
Look for the largest perfect square that divides 72. Perfect squares: 1, 4, 9, 16, 25, 36...
2
Factor 72
72 = 36 × 2. We use 36 because it's the largest perfect square factor of 72.
72 = 36 × 2
3
Apply the square root property
Use √(ab) = √a × √b to split the radical: √72 = √(36 × 2) = √36 × √2
√72 = √36 × √2
4
Simplify the perfect square
√36 = 6 (because 6 × 6 = 36)
√36 = 6
5
Write the final answer
√72 = 6√2
√72 = 6√2
6
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.
Ready to Practice Square Roots?
Generate a personalized practice test with MathQuizily. Get instant PDF downloads with answer keys.