What do you want to understand today?

PEAZIT Aha card

Squaring finds an area; a square root finds the side

a² means a × a. The principal square root √b is the non-negative number whose square is b.

For a square, move between side length and area.

Side a	Area a²	Back to the side
3	9	√9 = 3
5	25	√25 = 5
7	49	√49 = 7

One worked example

6² = 6 × 6 = 36Squaring is not multiplying by 2.
√36 = 6Find a non-negative number whose product with itself is 36.
(−6)² = 36 tooThe equation x² = 36 has two solutions, but √36 denotes only 6.

Watch out: In the real numbers, square roots require non-negative inputs. √(a²) = |a|, so √((−3)²) = 3.

Goal, prerequisites and card origin

What you will learn: Distinguish squaring from taking a square root.

What you need first: Multiplication and the area of a square.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

Pythagoras: squares on the sides

Right angle — is formed by the two — Legs a = 3, b = 4

Right angle — opposite it lies the — Hypotenuse c

Legs a = 3, b = 4 — square areas 9 and 16 are added — a² + b² = c²

Hypotenuse c — its square has area 25 — a² + b² = c²

a² + b² = c² — take the square root to recover length — c = √25 = 5

a² means a × a. The principal square root √b is the non-negative number whose square is b.

Without JavaScript, write your answer elsewhere before opening the solution.What is √64?

Solution — open after your own attempt

8 8 × 8 = 64, and √64 denotes the non-negative square root.

A question for your next return: What is 11²?

Solution — open after your own attempt

121 11² = 11 × 11 = 121.

Catalogue

Book

WikibooksEN

Basic Algebra/Solving Quadratic Equations/Solving Quadratic Equations By Taking The Square Root of Both Sides

Link to the page “Basic Algebra/Solving Quadratic Equations/Solving Quadratic Equations By Taking The Square Root of Both Sides” in Wikibooks. Subject assignment uses its title and source categories.