# Cancelling Squares: Can It Be Done?

• PhYsIcAlLy QuAnTuM
In summary, the conversation is about whether or not it is valid to cancel the squares on either side of an equation. The speaker's argument is that by taking the square root of both sides, the squares can be cancelled, resulting in a simplified equation. However, others argue that this is not a valid method. The speaker asks for opinions from their friends and gives an example to support their argument.
PhYsIcAlLy QuAnTuM
Greetings friends,

I have come across an argument on cancelling the squares on either side of an equation. For example if the equation is (a-b)^2=(c-b)^2 my argument is that i can cancel the squares by taking the square root of both sides as to get (a-b)=(c-b) and hence a=c. But others says that squares cannot be remove as such. So I thought i would consult you guys. What do you think, am i wrong or are they wrong?

thanx for your help!

A^2=B^2 then that tells us that A^2-B^2 = 0, or that (A-B)(A+B) = 0, and so we have that either A=B, or A=-B.

This is rather evident since, consider that (-2)^2=2^2.

In other words, if (a-b)^2= (c-d)^2 then EITHER a-b= c-d OR a-b= d-c.

## 1. Can all squares be cancelled?

No, not all squares can be cancelled. It depends on the numbers used to create the square and the method of cancellation being used.

## 2. How do you cancel a square?

The most common method of cancelling a square is by finding the factors of the number and using those factors to create a new square. For example, the square of 36 can be cancelled by finding the factors 4 and 9, and using them to create the new square 2x3=6.

## 3. Is it possible to cancel a square with a prime number?

No, it is not possible to cancel a square with a prime number. Prime numbers only have two factors (1 and itself), so it is not possible to find two factors to create a new square.

## 4. Can you cancel a square with negative numbers?

Yes, it is possible to cancel a square with negative numbers. The process is the same as cancelling with positive numbers, but the resulting square will also be negative.

## 5. Are there any other methods for cancelling squares?

Yes, there are other methods for cancelling squares, such as using algebraic equations or using the square root function. However, these methods may not work for all types of squares and may require more advanced mathematical knowledge.

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