Perfect squares & square roots
A perfect square is a whole number times itself, like 7² = 49. A square root reverses that: √49 = 7. If a square's area is 49 cm², each side is 7 cm.
How to answer questions
- For a perfect square, ask: “What nonnegative number times itself makes this?”
- For a number between squares, find the perfect squares just below and above it.
- Use their square roots as bounds, then estimate more closely if asked.
Worked example
Estimate √50: 49 < 50 < 64, so
√49 < √50 < √64 → 7 < √50 < 8Because 50 is close to 49, √50 ≈ 7.1.
How to prepare
Memorize the squares from 1² through 12². Sketch a square to connect its side length with its area.
Which is a perfect square, 49 or 50? Estimate √11 between two whole numbers.
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More practice · 3 questions
Try all three before you open the solutions.
Find √121.
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11 × 11 = 121, so √121 = 11.
Between which two whole numbers is √30? Estimate to one decimal place.
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25 < 30 < 36, so 5 < √30 < 6. Since 5.5² = 30.25, √30 is about 5.5 to one decimal place.
A square has an area of 144 cm². What is the length of one side?
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The side length is the square root of the area. √144 = 12, so each side is 12 cm.