Square Roots and Perfect Squares
Perfect squares are numbers that are products of equal factors: 36 = 6 × 6. Their square roots undo that squaring: √36 = 6. Non-perfect squares produce irrational numbers — students get their first encounter with numbers that go on forever without repeating. The Pythagorean theorem gives square roots immediate geometric meaning.
What students explore
Perfect squares are numbers that are products of equal factors: 36 = 6 × 6. Their square roots undo that squaring: √36 = 6. Non-perfect squares produce irrational numbers — students get their first encounter with numbers that go on forever without repeating. The Pythagorean theorem gives square roots immediate geometric meaning.
Key ideas
Identify perfect squares to 144. Determine the square root of a perfect square. Estimate the square root of a non-perfect square to the nearest tenth. Apply the Pythagorean theorem to find missing side lengths.
Putting it together
Apply these ideas through hands-on activities, guided practice, and real-world problems.