Surds

Question 1

rational numbers

Answer 1

numbers that can be expressed as fractions with integer numerators and denominators and are expressed as decimals that recur or terminate. eg. 1.6, 2.7 (27/10), 0.9, 3/7, -3, -4/39.

Question 2

irrational

Answer 2

numbers that cannot be expressed as fractions with integer numerator and denominators and are expressed as infinite non recurring decimals. e.g √3

Question 3

expressing surds as a positive number

Answer 3

means in: √positive integer
1. sqaure coefficient and put it under the square
2. times like a normal surd

Question 4

simplifying surds

Answer 4

1. break surd into factors (square factors if possible
2. simplify
   (simplifying surds does not mean solving them)

Question 5

adding + subtracting surds

Answer 5

like surds can be added or subtracted as long as they are under the same root and the same denominator (do this first of applicable).
e.g 3√3 + 5√3 = 8√3
3√5/2 + 2√5/2 = 5√5/6

Question 6

multiplying + dividing surds

Answer 6

Multiplication:
1. coefficients multiplied
2. surds multiplies
3. surds simplified

Division:
1. put under the same fraction root e.g √-10/2
2. simplify
OR
1. put coefficients as fraction and surds as fraction so they are separated.
2. simplify coefficient fraction
3. simplify surd fraction

Question 7

rules

Answer 7

(√x)^2 = x
√x^2 = x

Answer 8

√2 x √2 = 2
√11^2 = 11

Question 9

Why Rationalise Surds?

Answer 9

Makes denominator a whole number

Question 10

Rationalising surds

Answer 10

multiply surd by itself to cancel out surd. Simplify if necessary.

Question 11

brackets with surds

Answer 11

1. expand like normal equation
2. simplify by splitting up surd