 # Intermediate Algebra Tutorial 37

Intermediate Algebra Answer/Discussion to 1a The thought behind this is that we are looking for the square root of . This means that we are looking for an expression that, when we square it, we get What do you think it is?

Let's find out if you are right: Since squared is , is the square root of  Answer/Discussion to 1b The thought behind this is that we are looking for the cube root of . This means that we are looking for an expression that, when we cube it, we get .

What do you think it is?

Let's find out if you are right: Since cubed is  is the cube root of  Answer/Discussion to 1c The thought behind this is that we are looking for the fourth root of . This means that we are looking for an expression that, when we raise it to the fourth power,  we get .

What do you think it is?

Let's find out if you are right: Since raised to the fourth power is and there is a negative in front of the radical, is the negative fourth root of  Answer/Discussion to 1d The thought behind this is that we are looking for the fifth root of .  This means that we are looking for an expression that, when we raise it to the fifth power, we get What do you think it is?

Let's find out if you are right: Since raised to the fifth power  is  is the fifth root of . Answer/Discussion to 2a Since it didn't say that x or y are positive, we have to assume that they can be either positive or negative.  Since the root number and exponent are equal, then we can use the rule. Since the root number and the exponent inside are equal and are the even number 2, then we need to put an absolute value around x - y for our answer.  The reason for the absolute value is that we do not know if x or y are positive or negative.  So if we put x - y as our answer and it was negative, it would not be a true statement. Answer/Discussion to 2b Since the root number and exponent are equal then we can use the rule. This time our root number and exponent were both the odd number 3.  When an odd numbered root and exponent match, then the answer is the base whether it is negative or positive.