PEAZIT Aha card
Go straight to resources ↓Square roots: extract a perfect square
For nonnegative a, b, √(ab) = √a · √b. Find a large perfect-square factor inside the root.
| Expression | Meaning |
|---|---|
| √72 = √(36 · 2) | 36 is a perfect square. |
| √36 · √2 | Split the product into two square roots. |
| 6√2 | The square root of 36 is 6. |
One worked example
- √72 = √(36 · 2)36 is a perfect square.
- √36 · √2Split the product into two square roots.
- 6√2The square root of 36 is 6.
Watch out: This does not work for sums: √(a + b) generally is not √a + √b. Also, √(x²) = |x|.
Goal, prerequisites and card origin
What you will learn: Simplify a square root using a perfect-square factor.
What you need first: Square roots and small perfect squares.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
For nonnegative a, b, √(ab) = √a · √b. Find a large perfect-square factor inside the root.