Last reviewed: 11 November 2026
Updated November 2026. These Grade 7 squares and square roots notes show how to square whole numbers, fractions and decimals by multiplication, and how to find square roots of perfect squares by factors, by division or with a calculator. A square is a number multiplied by itself: 132 = 13 × 13 = 169. A square root reverses that step: √169 = 13, because 13 × 13 = 169.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 7 Mathematics numbers sub-strand on squares and square roots in the KICD Grade Seven curriculum designs. Using mathematical tables for squares that are not obvious by hand is later work, in the Grade 8 squares and square roots notes. For Grade 7 topics overall, use the Grade 7 mathematics revision guide and the Grade 7 notes hub.
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Squares of Whole Numbers, Fractions and Decimals
To square a number, multiply it by itself. You can use a grid, long multiplication or a calculator. For a fraction, square the numerator and the denominator separately: (a/b)2 = a2/b2. For a decimal, multiply as usual and count the decimal places. OpenStax Prealgebra’s section on square roots starts from the same “multiply a number by itself” definition.
Worked example
132 by long multiplication: 13 × 10 = 130 and 13 × 3 = 39, then 130 + 39 = 169.
(3/4)2 = 9/16.
(0.6)2 = 0.36, because 6 × 6 = 36 and two decimal digits in the factors give two in the product. Notice that 0.6 = 3/5 and (3/5)2 = 9/25 = 0.36, a useful check.
Square Roots of Perfect Squares
A perfect square is the square of an integer, a fraction of integers, or a decimal that multiplies neatly, such as 1.21 = 1.1 × 1.1. Methods you are expected to use include:
- factors: write the number as a product of prime factors and pair them;
- division (repeated subtraction of odd numbers, or long division for roots);
- a calculator, when your teacher allows it.
Worked example: factors
√196. 196 = 2 × 98 = 2 × 2 × 49 = 22 × 72. Pairing the primes gives √196 = 2 × 7 = 14.
√(36/100) = √36 / √100 = 6/10 = 0.6.
√1.21 = 1.1, because 1.1 × 1.1 = 1.21.
Not every number you meet is a perfect square. Grade 7 asks you to find roots of those that are; estimating roots of other numbers is not the main task here.
Original Practice Questions With Worked Answers
- Work out 152. 15 × 15 = 225.
- Work out (5/6)2. 25/36.
- Work out (0.7)2. 0.49.
- Find √81. 9, because 9 × 9 = 81.
- Find √225 by prime factors. 225 = 32 × 52, so √225 = 3 × 5 = 15.
- A square classroom floor has area 64 m2. How long is one side? √64 = 8 m.
Cover the answers and try each question. Squaring decimals uses the same place-value care as the Grade 7 decimals notes. For timed practice use the Grade 7 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 square a fraction?
Square the top and the bottom separately. (3/4)2 = 9/16. You can think of it as (3/4) × (3/4).
What is a perfect square?
It is a number that is the square of another number you already know, such as 169 = 132 or 9/16 = (3/4)2. Grade 7 square roots concentrate on these.
How do you find a square root by factors?
Write the number as a product of primes and pair equal factors. 196 = 22 × 72, so √196 = 2 × 7 = 14.
Is a calculator allowed for squares and square roots?
The Grade 7 design includes calculators as one of the methods, along with grids, long multiplication, factors and division. Follow your teacher’s instruction for tests.