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Adding and Subtracting Surds. Slideshow 8, Mr Richard Sasaki, Room 307. Objectives. 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. Index Form.

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Adding and subtracting surds

Adding and Subtracting Surds

Slideshow 8, Mr Richard Sasaki, Room 307


Objectives
Objectives

  • 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


Index form
Index Form

  • Let’s review some rules about index form.

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


Index form1
Index Form

  • 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.


Simplifying surds
Simplifying Surds

  • 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).



Adding and subtracting surds1
Adding and Subtracting Surds

  • 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.


Adding and subtracting surds2
Adding and Subtracting Surds

  • 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.


Adding and subtracting surds3
Adding and Subtracting Surds

  • Example

  • Can we simplify ?

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

Simplify


Answers1
Answers

  • Let .

  • .

  • This is one method…

  • But .

  • .

  • or


Answers2
Answers

  • and

  • and

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

to 3 s.f each.