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Is there any rational number whose square is 2?

We all know the the square root of 2 is irrational. So, the answer should be no. But how do we prove it?Let's assume for contradiction that x 2 =2 and that x is rational. Then x can be expressed as a rationa...
AS
Answered by Andrei S. • Maths tutor
13475 Views

Is a positive integer even if its square is even?

Let's take a positive integer n.We can write it as a product of prime numbers:n=p 1 p 2 ...p r , where p 1 , p 2 , ..., p r are prime factors of n.Now, assume that n 2 is even. Then one of the p i equals 2. ...
AS
Answered by Andrei S. • Maths tutor
3809 Views

How do signs change in an inequality?

Normal manipulation of inequalities does not affect the direction of the inequality such as: addition subtraction multiplication or division by a positive number, The direction of the inequality will change ...
OZ
Answered by Oscar Z. • Maths tutor
12524 Views

How do I find the cartesian equation for a curve written in parametric form?

Reminder - a cartesian equation is written in terms of x and y (e.g. y = 2x + 3) while parametric equations are written with x and y separately in terms of t. Example: Find the cartesian equation of the curv...
AO
Answered by Alexis O. • Maths tutor
11749 Views

Finding stationary points

Finding stationary points. You can find stationary points on a curve by differentiating the equation of the curve and finding the points at which the gradient function is equal to 0. One way of determining a...
JF
Answered by Jessica F. • Maths tutor
15054 Views