Solve by square rootsX² = p and ax² = c
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Solve each equation by taking square roots.
1x² = 49
2x² = 100
3x² = 36
47x² = 28
55x² = 180
6x² = 121
7x² = 4
82x² = 200
99x² = 225
102x² = 50
Solving x² = p by square roots worksheets
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.
If they get stuck
Solving x² = p by square roots
The answer key prints on a separate page.
What's on this sheet
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 a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Solving x² = p by square roots, step by step