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How do I prove that an irrational number is indeed irrational?

[NOTE: An irreducible fraction (or fraction in lowest terms) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1.] Given that p is a prime, positive in...
LD
Answered by Liam D. • Maths tutor
9839 Views

How do I rationalise the denominator of a fraction which consists of surds?

[ Recall: the numerator of a fraction is the top number; the denominator refers to the bottom number. A surd is an irrational number, e.g. √3, √5, etc.]Given the following fraction:(a+√b)/(c-√b), where a,b a...
LD
Answered by Liam D. • Maths tutor
10656 Views

Given that y = x^4 + x^(1/3) + 3, find dy/dx

We use the rule that if y = x^n then dy/dx = n*x^(n-1) which is valid whether or not n is an integer. We also use that differentiation is a linear operation, which means that we can differentiate term by ter...
KS
Answered by Karan S. • Maths tutor
15567 Views

What is the cosine rule?

What is it? The cosine rule is a tool to find the size of an angle or the length of a side in a triangle. When to use it? - When we are given 2 sides and an angle- When we are given 3 sides How? For a triang...
NG
Answered by Naomi G. • Maths tutor
5721 Views

How do I use Pythagorus' Theorum?

Pythagorus' Theorum is used to calculate the lengths of the sides of a right angled triange, and is written mathematically as follows: a 2 + b 2 = c 2 The letters (a, b and c) each stand for one of the three...
NP
Answered by Narissa P. • Maths tutor
7147 Views