Simplifying Surds Flashcards

All 7 cards in this deck

What are the steps to simplify a single surd?

e.g. simplify $\sqrt{12}$

1. Find the largest square factor: $12 = 4 \times 3$
2. Split the root: $\sqrt{12} = \sqrt{4} \times \sqrt{3}$
3. Root the square factor: $2\sqrt{3}$

What must you do before you can add or subtract two surds?

e.g. $\sqrt{80} - \sqrt{5}$

Simplify each surd so the surd parts are the same, then combine the numbers in front.
$4\sqrt{5} - \sqrt{5} = 3\sqrt{5}$

What is $\sqrt{a} \times \sqrt{b}$ equal to?

e.g. $\sqrt{2} \times \sqrt{8}$

$\sqrt{ab}$
$\sqrt{2} \times \sqrt{8} = \sqrt{16} = 4$

True or false? $\sqrt{a} + \sqrt{b} = \sqrt{a+b}$

False. Surds cannot be combined that way; e.g. $\sqrt{9} + \sqrt{16} = 7$ but $\sqrt{25} = 5$.

What are the steps to expand and simplify a squared surd bracket?

e.g. $(2+\sqrt{3})^2$

1. Write as two brackets and expand all four terms: $4 + 2\sqrt{3} + 2\sqrt{3} + 3$
2. Use $(\sqrt{a})^2 = a$, so $\sqrt{3}\times\sqrt{3}=3$
3. Collect like terms: $7 + 4\sqrt{3}$

What does it mean to give a length or an area in exact form (surd form)?

Leave any square root as a fully simplified surd rather than rounding it to a decimal.
e.g. a square of area $50$ cm$^2$ has side $5\sqrt{2}$ cm.

A student simplifies $\sqrt{12}$ as $3\sqrt{2}$. What is the error?

$12 = 4 \times 3$, so $\sqrt{12} = \sqrt{4}\times\sqrt{3} = 2\sqrt{3}$, not $3\sqrt{2}$.