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Grade 5 Math · Level 5, Patterns & Percents

Roots, Radicals & the Pythagorean Theorem

How the lesson starts: Roots, Radicals & the Pythagorean Theorem

1. Knight Ivy's ladder

   Knight Ivy needs to fix the flag on top of the castle wall. The wall is 8 feet tall, and her ladder stands 6 feet away. How long must the ladder be? We'll need squares and square roots!

2. Squares and square roots

   Here's a square garden 7 tiles long and 7 wide: 7 × 7 = 49 tiles. So 7² = 49. A square root works backward: 49 tiles make a square with sides of 7. So √49 = 7. Watch out: √64 is 8, not half of 64!

3. Cube roots

   Stack little cubes into a big cube: 3 long, 3 wide and 3 tall. That's 27 cubes! 3 × 3 × 3 = 27, so the cube root of 27 is 3. Also, ∛8 = 2 and ∛64 = 4.