When a quadratic is already a bare square, there is nothing to factor: isolate the square and take the root of both sides. These free printable worksheets solve x² = p and ax² = c that way, and every one has two answers.
The square root method starts here, with the square standing alone. For x² = 49 you take the root of both sides and get x = ±7; for 3x² = 48 you divide by 3 first to reach x² = 16, then root to x = ±4. The move that must never be dropped is the ±, because a positive number has two square roots and both are answers — a child who writes only +7 has found half the solution, and every step-by-step walk here writes the ± before it reports either root.
Why this sheet works
This is the entry form of the method, kept apart from the shifted version so the ± becomes a reflex before a subtraction is added around it. It also sits a step before factoring: the factoring sheets take x² + bx + c = 0, which these never print, and these take the bare squares, which those never print — so a child learns to tell the shapes apart.
How this one works
One question from this sheet, worked through a step at a time.
Solve x² = 49
x = ±√49=±7
x = 7orx = −7
Take the square root of both sides — and keep both signs: x = ±√49 = ±7.
Solve by square roots · X² = p and ax² = cAnswer key
1. x² = 49 → x = −7 or x = 72. x² = 100 → x = −10 or x = 103. x² = 36 → x = −6 or x = 64. 7x² = 28 → x = −2 or x = 25. 5x² = 180 → x = −6 or x = 66. x² = 121 → x = −11 or x = 117. x² = 4 → x = −2 or x = 28. 2x² = 200 → x = −10 or x = 109. 9x² = 225 → x = −5 or x = 510. 2x² = 50 → x = −5 or x = 5
