This course starts with the square of a number and the squares from 1 to 30, with short cuts for multiples of ten and numbers ending in 5. You then meet the square root as the opposite of squaring and learn two ways to find it: pairing prime factors, and the long division method that works for any number. Along the way you solve puzzles about trees in rows and soldiers in squares. The rules of square roots show what you may and may not do, and the course ends with square roots of decimals and fractions and with roots like √2 found to two decimal places.
Primary Years
Squares and Square Roots
Squares and perfect squares, square roots by prime factorisation and long division, the rules of square roots, and roots of decimals, fractions and numbers that are not perfect squares.
- 6 lessons
Overview
Lessons
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Squares of numbers
What a² means, the squares from 1 to 30, and patterns that help: squares near 25, multiples of 10, numbers ending in 5, sums of odd numbers and the last digit of a square.
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Square roots
The square root undoes squaring. Learn the √ sign, the square roots of perfect squares up to 900, quick roots of numbers ending in 00 and 25, and everyday problems about squares.
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Square roots by prime factorisation
Break a number into prime factors, pair them up and take one from each pair. Also how to tell a perfect square and what to multiply or divide by to make one.
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Square roots by long division
Pair the digits, double the answer so far and find the next digit. Find large square roots, and the least number to add or take away to make a perfect square.
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Properties of square roots
Rules for multiplying and dividing square roots, why a over √a is √a, and the warnings: √a + √b is not √(a + b), and a² + b² is not (a + b)².
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Square roots of decimals and fractions
Find square roots of decimals and fractions, use long division with decimals, and find roots that never end, such as √2 and √5, correct to two decimal places.
Practice papers
Ten question papers that follow the lessons in order. Each has 20 questions for 50 marks (1 hour 30 minutes), with a key sheet and worked solutions.
MCQ tests
Ten tests of 25 multiple-choice questions (30 minutes each). Answer them on the page and check your score, or download the PDF with its key and solutions.
Class notes
Squares and Square Roots
Typed from the teacher's handwritten class slides, 9 pages.
Download the notes (PDF, 370.3 KB)