# Simplified Radical Form with square and cubed roots

• dmnalgebra
In summary, the conversation revolves around difficulties in simplifying radicals on a new Ti-nspire Cx CAS calculator. The user is experiencing trouble with the calculator not showing the correct simplified form, even after adjusting settings and using parentheses. It is suggested to check the calculation mode, which may need to be set to CAS in order to correctly simplify radicals.

#### dmnalgebra

I just got a new Ti-nspire Cx CAS calculator and I am having trouble with being able to express a Radical in simplified form when there are exponents and variables of x and y. My problem is that this calculator will not show the simplified form correctly. I have taken others advice in setting the calculator to exact mode but I suspect that the other settings in this same area are wrong.

I currently have the settings at: Display Digits-Float 6, Angle-Degree, Exponential Format-Normal, Real or Complex-Real, Calculation Mode-Exact, Vector Format-Rectangular, Base-Decimal, Unit system-Eng/US.

Does anyone know what all of the settings should be? Any advice would be helpful at this point.

Example issue is that when I enter:
√68x2y I get 8√x5y and the correct answer is 8x2√xy and incase my typed questions are confusing, the x2, x5, x2 - the 2,5,2 are exponents.

Thanks

dmnalgebra said:
I just got a new Ti-nspire Cx CAS calculator and I am having trouble with being able to express a Radical in simplified form when there are exponents and variables of x and y. My problem is that this calculator will not show the simplified form correctly. I have taken others advice in setting the calculator to exact mode but I suspect that the other settings in this same area are wrong.

I currently have the settings at: Display Digits-Float 6, Angle-Degree, Exponential Format-Normal, Real or Complex-Real, Calculation Mode-Exact, Vector Format-Rectangular, Base-Decimal, Unit system-Eng/US.

Does anyone know what all of the settings should be? Any advice would be helpful at this point.

Example issue is that when I enter:
√68x2y I get 8√x5y and the correct answer is 8x2√xy and incase my typed questions are confusing, the x2, x5, x2 - the 2,5,2 are exponents.
That's not all that's confusing. One way to indicate exponents here at Physics Forums is to use the caret character ^. So x^2 represents the square of x, and so on.

With √68x2y, it's not clear what is under the radical.

This looks to me like √6 ##\cdot## 8x2 ##\cdot## y, but it could also be √(68) ##\cdot## x2 ##\cdot## y, or any of several other possibilities.

Since your answers come out with 8 and some other factors, the number must be 64, not 68 as you show.

If this is the expression you're working with -- √(64x^2 y)-- , then you should end up with 8x √y.

The problem that I'm working with is actually √(64x^5 y) and the correct answer is 8x^2√xy
I realize that 8(8) is 64 and that I have to borrow one from five and show the square root of four, which is two, leaving a remainder of one, thus the reason for 8x^2√xy but my calculator will not show the correct answer.

Sorry about the confusion. I am new at this calculator. Can you tell me why the Ti-nspire Cx CAS will not simplify it showing the correct answer?

dmnalgebra said:
The problem that I'm working with is actually √(64x^5 y) and the correct answer is 8x^2√xy
This really should be 8x^2√(xy), with the parentheses used to show that the square root is of the product xy, not just x.
dmnalgebra said:
I realize that 8(8) is 64 and that I have to borrow one from five and show the square root of four, which is two, leaving a remainder of one, thus the reason for 8x^2√xy but my calculator will not show the correct answer.
I'm guessing that you might not be using parentheses when you enter the expression. I don't have one of these calculators, so I can't say for sure.

If you enter √(64x^5y) it should produce 8x^2√(xy).

dmnalgebra said:
Sorry about the confusion. I am new at this calculator. Can you tell me why the Ti-nspire Cx CAS will not simplify it showing the correct answer?

I tried it with parentheses and it produces 8√x^5y and it should produce 8x^2√xy
I wish I could figure this out. It can't be that hard. If anyone reads this and knows how to get the Ti-nspire CX CAS to do this, please let me know. Thanks

## 1. What is simplified radical form with square and cubed roots?

Simplified radical form with square and cubed roots is a way to express a number that contains both square and cubed roots in its simplest form. This means that there are no perfect square factors inside the square root, and no perfect cube factors inside the cube root.

## 2. How do you simplify a radical form with square and cubed roots?

To simplify a radical form with square and cubed roots, you need to identify any perfect square or cube factors inside the radical and take them out. The remaining number inside the radical should be the smallest possible number that cannot be simplified further.

## 3. Can you provide an example of simplifying a radical form with square and cubed roots?

Yes, for example, to simplify √27, we first identify that 27 is a perfect cube. So, we can write it as √(3² x 3) = 3√3. Similarly, to simplify ∛75, we can write it as ∛(5² x 3) = 5∛3.

## 4. Why is it important to simplify radical form with square and cubed roots?

Simplifying radical form with square and cubed roots makes it easier to work with these numbers in mathematical calculations. It also helps in identifying patterns and relationships between different numbers.

## 5. Can a simplified radical form have both square and cubed roots together?

No, a simplified radical form cannot have both square and cubed roots together. It can only have either a square root or a cubed root, but not both at the same time. This is because the square root and cubed root are inverse operations of each other, and they cancel each other out.

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