Surds

Question 1

Index Rules,

power of 0

power of 1

multiplying powers

dividing powers

raising powers

negative powers

surds and powers

Answer 1

Any number to the power of 0 is 1

Any number to the power of 1 is itself

When multiplying powers, add the powers, given the base is the same

When dividing powers, subtract the powers, given the base is the same

When raising to a power (index is outside of bracket), multiply the power

If a power is negative it is equal to its reciprocal with the inverse of the power (positive power)

Surds can be written in index form,,
eg.
3√(2^5) is the same as 2^(5/3)

Question 2

Surd Rules,

multiplying surds
dividing surds
multiplying similar surds

simplifying surds

surds with the same root sign

multiplying and dividing surds

Answer 2

√(a x b) = √a x √b
√(a/b) = √a / √b
√a x √a = a

Surds can be simplified if the number under the surd sign is a multiple of a perfect square, the aim is to have the lowest possible number under the surd sign

Surds with the same root sign can be added or subtracted

When multiplying or dividing surds, multiply the numbers under the root signs

Question 3

Rationalising Surds,

purpose

process

Answer 3

When surds are rationalised we remove the surd from the denominator, hence the term rationalising the denominator

To rationalise the denominator you multiply the fraction by the same surd

Question 4

Conjugate Surds,

meaning

process of rationalising

conjugate surd rules

Answer 4

A conjugate surd is a fraction which has a denominator containing a surd and a number

Multiply the fraction with a similar surd with a different expression for the number

a + √b has a conjugate of a - √b
a - √b has a conjugate of a + √b