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11 Squares and Square Roots

Notes

The use of primes to give exact expressions for whole numbers or product of primes is illustrated numerically with the aid of a few algebraic description of some rules. Viewers should try to understand both numerical patterns and the algebraic formulas.

1. Squares and Square Roots Introduction. After listing or calculating the squares of whole numbers 0 to 13, 15 and 20, the square roots of the squares is given. The square root of 196 = 4 × 49 is also found. The lesson as a whole serves as introduction.

2. Square Roots with Primes shows how to calculate and represent square roots of whole numbers by finding the prime factorizations.

3. Properties of Square Roots with examples Two properties of square roots are presented algebraically, and then use. In the use, viewers should note or identify the roles played by each letter present in the properties. Teachers and tutors may show how the formulas are used by identifying in each example the formula used and the values given the symbols in each formula. That may develop or reinforce algebraic reasoning skills.

4. Square Roots with primes - more. Numerical examples of the properties in the previous lesson are given and followed by a single algebraic example. Here primes appear to the power 1 or 2.

5. Square Roots with primes - more still. This video shows how to to transform square roots of products of primes - the prime factorization of some numbers - into a standard form. Primes to powers greater than 2 appear.

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science