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Adding and Subtracting Surds

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Adding and Subtracting Surds

Slideshow 8, Mr Richard Sasaki, Room 307

- Be able to convert numbers in index form into fractions and surds
- Understand the values of surds that cannot be simplified
- Be able to add and subtract surds together

- Let’s review some rules about index form.

- Writing numbers in surd form can help us simplify them further.

- Examples

- Write in surd form.

- Write in surd form.

- Just try to remember that and . If is a surd then the denominator must be changed to an integer.

- Surds are often in the form…

- Radicand

- If is in its simplest form, what values can take?

- 10,

- 6,

- 5,

- 2,

- 3,

- 7,

- …

- These are the numbers that do not have square factors (other than 1).

- Example

- How can we simplify ?

- If the radicands are the same, we can easily add roots together.

Simplify

- If there are fractions, we need to make the denominators the same too.

- Example

- How can we simplify ?

- If the radicands are the same, we can easily add roots together.

Simplify

- If there are fractions, we need to make the denominators the same too.

- Example

- Can we simplify ?

- No we can’t. Both and are in their simplest forms. So we just leave it the same.

Simplify

- Let .
- .

- This is one method…
- But .
- .

- or

- and

- and

The radicand multiplied by 100 gives the same result multiplied by 10. (i.e if .

to 3 s.f each.