Surds and decimals and stuff- Term 2

Question 1

What is a surd?

Answer 1

A surd is a square root of an integer that does not give you an integer answer

Question 2

What is the surd law?

Answer 2

\/ab = \/a \/b

Question 3

Simplify \/75

Answer 3

Find a pair of numbers with one a square number
\/25x3
=\/25 \/3
=5 \/3

Question 4

Simplify \/32

Answer 4

= \/16x2
=4 \/2

Always go for the biggest root

Question 5

X1/2 x X1/2=?

Answer 5

X^1= X

Question 6

\/X x \/X = ?

Answer 6

X

Question 7

\/x^2

Answer 7

X

Question 8

Expand and write in the form a+b \/c

\/2 (5+\/2)

Answer 8

5 \/2 +2

2 is because \/2 x \/2 = 2

Question 9

Expand and simplify

1+\/2)(3+\/2

Answer 9

=3+\/2+3\/2+2
=3+2+\/2+3\/2
=5+4\/2

Question 10

Expand and simplify

\/3-2)(4-\/3

Answer 10

=4\/3-3-8+2\/3
=4\/3+2\/3-3-8
=6\/3-11

Question 11

Rationalise the denominator

2/square root of 3

Answer 11

2/square root of three x \/3 = 2 square root of three/ 3

Turn it into an equivalent fraction

Question 12

What does it mean to rationalise the denominator?

Answer 12

To get rid of the surd on the denominator

Question 13

Rationalise the denominator and simplify

10/square root of 2

Answer 13

10/square root of 2 x \/2 = 10 square root of 2/ 2
10 square root of 2/ 2 divided by 2 = 5square root of 2/1
Ans: 5square root of 2
If the denominator is 1, you can take it out

Question 14

Convert 0.6recurring into a fraction

Answer 14

Let X = 0.6recurring. |. You’re letting X = 0.6
10x = 6.6recurring | times both sides by 10
10x =6.6recurring - x = 0.6recurring | they go on forever but 6-6=0
9x= 6.0
X = 6/9. | divide by nine
X = 2/3
Therefore 0.6recurring = 2/3

Question 15

Convert 0.24recurring into a fraction

Answer 15

Let X = 0.24recurring
10x=2.4recurring
100x=24.4recurring

100x=24.4recurring-
10x=2.4recurring
=
90x=22
(Both Divided by 90)
X=22/90
Therefore 2.4recurring = 22/90