surds

Question 1

what is a surd?

Answer 1

any type of root whose exact decimal or fraction cannot be found.

Question 2

what is an irrational number + are surds irrational?

Answer 2

irrational number = cannot be expressed in the form a/b.
surds are irrational

Question 3

negative square root?

Answer 3

undefined

Question 4

when x is positive:
(√x)^2 =

Answer 4

√x x √x = x

√x^2 = x

Question 5

for x>0 and y>0 (both positive):
√xy =

Answer 5

√x x √y

Question 6

you can only add and subtract ____ surds?

Answer 6

like

Question 7

you can only add and subtract ____ surds?

Answer 7

like

Question 8

multiplying and dividing surds?

for x>0 and y>0:
√x/y =

Answer 8

√x / √y

Question 9

how can you expand binomial products involving surds?

Answer 9

the same was as algebraic expressions

Question 10

(a + b)^2

Answer 10

a^2 + 2ab + b^2

Question 11

(a - b)^2

Answer 11

a^2 - 2ab + b^2

Question 12

difference of two squares?

Answer 12

(a + b)(a - b) =
a^2 - b^2

Question 13

how do you rationalise the denominator?

Answer 13

multiply the numerator and the denominator by the surd that appears in the denominator, then simplify