Last reviewed: 10 November 2026
Updated November 2026. These Grade 8 squares and square roots notes explain how to find squares and square roots of numbers from mathematical tables and with a calculator, and how to use them in real life. The square of a number is the number multiplied by itself: 23² = 529. The square root reverses this: √529 = 23. For numbers that are not perfect squares, use tables or a calculator: √50 ≈ 7.071.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 8 maths topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Squares and square roots is a sub-strand under Numbers in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners work out squares and square roots of numbers from tables and with a calculator, and use them in real-life situations. The design is listed on the KICD Grade Eight curriculum designs page. (In Grade 7, learners found squares and square roots of perfect squares by multiplication and factors.)
Squares and Square Roots: The Basics
Squaring and finding a square root are inverse operations, as explained in OpenStax Prealgebra’s section on square roots.
| n | 11 | 12 | 13 | 14 | 15 | 20 | 25 |
|---|---|---|---|---|---|---|---|
| n² | 121 | 144 | 169 | 196 | 225 | 400 | 625 |
Decimals: 0.7² = 0.49, so √0.49 = 0.7. Fractions: √(9/16) = 3/4. A square root sign means the positive root.
Using Tables of Squares
Tables of squares usually cover numbers from 1.000 to 9.999. For numbers outside that range, write the number in standard form, read the table, then adjust.
Worked example: square of 47.3
- 47.3 = 4.73 × 10.
- From tables (or by multiplication), 4.73² ≈ 22.37.
- 47.3² = 22.37 × 10² ≈ 2,237.
Check with an estimate: 47² is a little more than 45² = 2,025 and less than 50² = 2,500. The answer fits.
Worked example: square of 0.36
0.36 = 3.6 × 10⁻¹. 3.6² = 12.96. So 0.36² = 12.96 × 10⁻² = 0.1296.
Using Tables of Square Roots
Square-root tables usually have two parts: one for numbers 1 to 10 and one for 10 to 100. Group the digits in pairs from the decimal point to decide which part to use.
Worked example: √2,500
2,500 = 25 × 10². √25 = 5, so √2,500 = 5 × 10 = 50.
Worked example: √500
500 = 5 × 10². √5 ≈ 2.236, so √500 ≈ 22.36. Note that 500 = 5 × 100, not 50 × 10: you need an even power of 10 so its square root is a whole power of 10.
Using a Calculator
Use the x² key for squares and the √ key for square roots. Some calculators need you to press √ before the number. Always estimate first: √50 is between 7 (√49) and 8 (√64), and close to 7, so a calculator answer of 7.071 makes sense. If you get 25, you may have pressed ÷2 instead of √.
Real-Life Uses
- Square rooms and plots: a square room of area 144 m² has sides of √144 = 12 m.
- Tiles: 400 square tiles of side 30 cm can cover a square floor of side √400 × 30 cm = 20 × 30 = 600 cm = 6 m.
- Pythagoras: the diagonal of a 5 m by 5 m square garden is √(25 + 25) = √50 ≈ 7.07 m. See our Pythagoras theorem notes.
Original Practice Questions With Worked Answers
- Find 1.5². 2.25.
- Find √0.81. 0.9.
- Use 6.2² = 38.44 to find 620². 38.44 × 10⁴ = 384,400.
- A square plot has area 2,025 m². Find its side. √2,025 = 45 m.
- Between which two whole numbers is √90? 9 and 10, because 81 < 90 < 100.
Cover the answers and attempt each question first. For timed practice, use the Grade 8 revision papers or the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
How do you find the square root of a number using tables?
Write the number as a value times an even power of 10, read the square root of the value from the tables, then multiply by the square root of the power of 10.
What is a perfect square?
A number that is the square of a whole number, such as 36 (6²) or 169 (13²).
How can I check a calculator answer for a square root?
Estimate between the nearest perfect squares, or square the answer to see if you get back the original number.
Is the square root of a number always smaller than the number?
No. For numbers between 0 and 1, the square root is bigger: √0.25 = 0.5.