Solve by square rootsSquare and shifted forms
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Solve each equation by taking square roots.
14x² = 324
2(x + 6)² = 4
3x² = 100
4(x − 5)² = 36
53x² = 363
6(x + 4)² = 16
7(x + 8)² = 100
8(x + 9)² = 49
9x² = 81
10x² = 25
Solving quadratics by square roots worksheets
Some quadratics do not need factoring: when the equation is already a square, you isolate it and take the square root of both sides. These free printable worksheets solve x² = p, ax² = c and (x − h)² = k that way — and every one has two answers.
If they get stuck
Solving quadratics by square roots
The answer key prints on a separate page.
What's on this sheet
This is the square-root method, the companion to the factoring sheets. The equation arrives as a square, so there is nothing to factor: for x² = 49 you take the root of both sides and get x = ±7; for 3x² = 48 you divide by 3 first, then root; for (x − 2)² = 9 you root both sides to x − 2 = ±3, then add 2. The one thing to keep is the ±, because a positive number has two square roots and the answer is both.
Why this sheet works
It comes a step before factoring and stays beside it: the factoring sheets take x² + bx + c = 0, which these never print, and these take the square forms, which those never print. A child who has met both knows which method a question is asking for by its shape.
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 quadratics by square roots, step by step