# Question from grade 9 math (online course)

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My son is taking a online grade 9 math course. It's through the government (Ontario) and basically you have 7 units that you submit and get a grade on. So no teacher per say.

My problem is his next assignment has some questions about inverse operations. Here is the question:

3. State the inverse operation for each of the underlined operations. A verbal description of each of the given operations is also provided. (5 marks total)

a. 18 – 12       (subtract 12)   (1 mark)

b.  4 ÷ –2         (divide by –2)   (1 mark)

c. (Picture didn't copy right)             (the square root of 25)   (1 mark)

d. –3 X 8        (multiply by 8 )   (1 mark)

e. 43                (4 cubed)   (1 mark)

For (c) the square root of 25 is equal to 5. There is no operation here. For (e) 4 cubed is 64. How can you have an inverse operation to 64. I can have my son email the 'teacher' and have him wait up approximately 3 days to here back. But you guys are much quicker.

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16 minutes ago, Julie Smith said:

3. State the inverse operation for each of the underlined operations. A verbal description of each of the given operations is also provided. (5 marks total)

c. (Picture didn't copy right)             (the square root of 25)   (1 mark)

e. 43                (4 cubed)   (1 mark)

For (c) the square root of 25 is equal to 5. There is no operation here. For (e) 4 cubed is 64. How can you have an inverse operation to 64. I can have my son email the 'teacher' and have him wait up approximately 3 days to here back. But you guys are much quicker.

The inverse of "square root" is to square, i.e. raise to the power of 2. Of course taking the square root, ie raising to the exponent 12, is an operation.

The inverse operation of "cube" is to take the cube root, i.e. raise to the exponent one third.

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Just now, regentrude said:

The inverse of "square root" is to square, i.e. raise to the power of 2.

the inverse operation of "cube" is to take the cube root, i.e. raise to the exponent one third.

But the question is "What is the inverse of the square root of 25" The question isn't what is the inverse operation to finding the square root.

Would the inverse of the square root of 25 be 5 to the power of 2? I just don't understand how "the square root of 25" is considered an operation, so I can't see how it can have an inverse operation.

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5 minutes ago, Julie Smith said:

But the question is "What is the inverse of the square root of 25" The question isn't what is the inverse operation to finding the square root.

Would the inverse of the square root of 25 be 5 to the power of 2? I just don't understand how "the square root of 25" is considered an operation, so I can't see how it can have an inverse operation.

But the square root sign indicates the operation. Just like the division signs and the minus signs in the other problems indicate the operation. Which has to be performed on something, the operand.

The inverse of the operation "subtract 12 from whatever" is "add 12 to whatever". The inverse of the operation "multiply whatever by 8" is "divide whatever by 8".

The inverse of the operation "draw the square root of whatever" is "raise whatever to the power of 2. " Just like you had no problem with the "whatevers" on which the operation is performed in the other problems, there needn't be one here either. You cannot have the operation without an operand, i.e. object the operation is acting ON.

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13 hours ago, Julie Smith said:

3. State the inverse operation for each of the underlined operations. A verbal description of each of the given operations is also provided. (5 marks total)

c. (Picture didn't copy right)             (the square root of 25)   (1 mark)

e. 43                (4 cubed)   (1 mark)

"State the inverse operation" (My answers, below). Gently, Julie, I think you are overthinking the instructions. As you typed them, it does say to state the inverse operation

c) the square of 5

e) the cube root of 64

In other words, I agree with regentrude.

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