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Simplifying Surds. Slideshow 6, Mr Richard Sasaki, Room 307. Objectives. Understand the meaning of rational numbers Understand the meaning of surd Be able to check whether a number is a surd or not Be able to simplify surds. Rationality.

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simplifying surds

Simplifying Surds

Slideshow 6, Mr Richard Sasaki, Room 307

objectives
Objectives
  • Understand the meaning of rational numbers
  • Understand the meaning of surd
  • Be able to check whether a number is a surd or not
  • Be able to simplify surds
rationality
Rationality

First we need to understand the meaning of rational numbers.

What is a rational number?

A rational number is a number that can be written in the form of a fraction.

is rational if where .

If where , we say . ( is in the rational number set, .)

rationality1
Rationality

irrational

If a number is not rational, we say that it is .

is irrational if it can’t be written in the form where .

Therefore, an irrational number .

Example

Show that 0.8 .

.

Note: If , .

answers
Answers

and .

.

where . .

where -3 and 3 are integers. .

Let and

Let and

Let and

surds
Surds

What is a surd?

A surd is an irrational root of an integer. We can’t remove its root symbol by simplifying it.

Are the following surds?

Yes!

Yes!

Yes!

No!

Even if the expression is not fully simplified, if it is a root and irrational, it is a surd.

multiplying roots
Multiplying Roots

How do we multiply square roots?

Let’s consider two roots, and where .

If we square both sides, we get…

If we square root both sides, we get…

, where .

simplifying surds1
Simplifying Surds

To simplify a surd, we need to write it in the form where is as small as possible and .

Note: Obviously, if .

Example

Simplify .

We try to take remove square factors out and simplify them by removing their square root symbol.

answers easy
Answers - Easy

Because has positive and negative roots anyway. .

No, of course not! is a surd but 6 is not prime.

Square numbers.

answers hard
Answers - Hard

Let be in the form where .

simplifies to or rather in the form . We can see , hence is not a surd.

1875

288

92

625

144

46

23

72

125

25

36

18

9