ASSIGNMENT 2 – SURDS (Solutions)

1) Express in terms of the simplest possible surds:

a) 50 = 𝟐𝟓 × 𝟐 = 𝟓 𝟐

b) 18 = 𝟗 × 𝟐 = 𝟑 𝟐

c) 200 = 𝟏𝟎𝟎 × 𝟐 = 𝟏𝟎 𝟐

2) Simplify:

a) 2(3 − 2) = 𝟑 𝟐 − ( 𝟐)𝟐 = 𝟑 𝟐 − 𝟐

b) 2 − 1 ( 2 + 1) = ( 𝟐)𝟐 − (𝟏)𝟐 = 𝟐 − 𝟏 = 𝟏

c) 3 3 − 2 3 3 + 2 = 𝟑 𝟑 𝟐− 𝟐 𝟐 = 𝟗 𝟑 − 𝟒 = 𝟐𝟑

3) Rationalise the denominators and simplify:

a) 1

3

= 𝟏

𝟑×

𝟑

𝟑=

𝟑

𝟑

b) 1

3−1

= 𝟏

𝟑−𝟏×

𝟑+𝟏

𝟑+𝟏=

𝟑+𝟏

( 𝟑)𝟐−(𝟏)𝟐=

𝟑+𝟏

𝟑−𝟏=

𝟑+𝟏

𝟐

c) 1

3+2 5

=𝟏

𝟑+𝟐 𝟓×

𝟑−𝟐 𝟓

𝟑−𝟐 𝟓=

𝟑−𝟐 𝟓

(𝟑)𝟐−(𝟐 𝟓)𝟐=

𝟑−𝟐 𝟓

𝟗−𝟒(𝟓)=

𝟑−𝟐 𝟓

−𝟏𝟏