Using Khan Academy videos and practice sets, I’ll attempt to construct a lesson on how to work with radicals for algebra students. The idea is to have students watch the videos and do the practice sets while I monitor their progress using the Academy’s Coaching pages.

Review of working with fractions (rational numbers)

Start with a review of adding and multiplying fractions.

Adding Fractions with a Common Denominator

The first topic — adding fractions –ought to be really easy for algebra students, but it allows them to become familiar with the Khan Academy website and doing the practice sets.

Now do the Practice Set.

OPTIONAL: Subtracting fractions with a common denominator works the same way. Students may do this practice set if they find it useful.

Adding Fractions with a Different Denominator

This is usually a helpful review.

The practice set.

Multiplying and Dividing Fractions

A good review that helps build up to working with radical numbers.

Multiplying fractions:

Do the multiplying fractions practice set.

Dividing Fractions:

Dividing fractions practice set.

Converting Fractions to Decimals

The last review is on how to convert fractions to decimals.

Now try the practice set for ordering numbers.

Finding Square Roots (Rational and Irrational)

Great video explaining how to find square roots.

Now practice simplifying radicals.

Quotient Property of Square Roots

Khan does not have a video or practice set for this topic, but it’s fairly straightforward:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

So, for example:
$\sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}$

You can also simplify first:
$\sqrt{\frac{12}{75}} = \sqrt{\frac{3 \cdot 4}{3 \cdot 25}} = \sqrt{\frac{\not{3} \cdot 4}{\not{3} \cdot 25}} = \sqrt{\frac{ 4}{25}} = \frac{2}{5}$

Now try the odd questions in section B of the written exercises (#21-31) of the textbook (Algebra 1: Structure and Method).

Rational to Radical Numbers