Quick check: is this the same? (Radicals)

[Audentes]

Are these two equations the same? the first one is my answer, but I checked the calculator and it has a slightly different answer. mathematically it seems like they both yield the same answer, but is the calculator’s answer properly “simplified” compared to mine? I’m asking in case my answer isn’t acceptable for my test Monday
thanks
flo

the first image is my answer, the second is the calculator’s answer, And the third image attached is the question these answers are for

 

[Deleted member 4993]

Are these two equations the same? the first one is my answer, but I checked the calculator and it has a slightly different answer. mathematically it seems like they both yield the same answer, but is the calculator’s answer properly “simplified” compared to mine? I’m asking in case my answer isn’t acceptable for my test Monday
thanks
flo

the first image is my answer, the second is the calculator’s answer, And the third image attached is the question these answers are for

In my opinion, those two answers are equivalent.

 

[Audentes]

In my opinion, those two answers are equivalent.

Okay thank you for clarifying!

 

[Dr.Peterson]

Are these two equations the same? the first one is my answer, but I checked the calculator and it has a slightly different answer. mathematically it seems like they both yield the same answer, but is the calculator’s answer properly “simplified” compared to mine? I’m asking in case my answer isn’t acceptable for my test Monday
thanks
flo

the first image is my answer, the second is the calculator’s answer, And the third image attached is the question these answers are for

For what it's worth, I prefer your answer, with a single radical. Calculators don't necessarily have a better aesthetic sense than people -- and that's really all this is, a matter of taste. As you say, they are equivalent.

Did you look in your textbook to see if they ever leave an answer looking like the calculator's version? I would expect their answers to look more like yours -- though even then, it wouldn't mean that other variations would be called wrong.

 

[Audentes]

Did you look in your textbook to see if they ever leave an answer looking like the calculator's version? I would expect their answers to look more like yours -- though even then, it wouldn't mean that other variations would be called wrong.

This specific assignment was from a virtual worksheet, but so far I haven’t seen my teacher split the radicals like the calculator.

For what it's worth, I prefer your answer, with a single radical. Calculators don't necessarily have a better aesthetic sense than people -- and that's really all this is, a matter of taste. As you say, they are equivalent.

ok thank you!

 

[HallsofIvy]

A little more detail. Yes, [math]\frac{3\sqrt{35x}}{10x}= \frac{3\sqrt{35}\sqrt{x}}{10x}[/math].

Now, \(\displaystyle \sqrt{35}= \sqrt{5}\sqrt{7}\) and \(\displaystyle 10= 5(2)\).

\(\displaystyle \frac{\sqrt{5}}{5}= \frac{1}{\sqrt{5}}\) and \(\displaystyle \frac{x}{\sqrt{x}}= \frac{1}{\sqrt{x}}\)
so that can be written \(\displaystyle \frac{3\sqrt{7}}{2\sqrt{5}\sqrt{x}}\).

However, many people prefer a "rationalized denominator" which is exactly the initial form.

 

[Audentes]

A little more detail. Yes, [math]\frac{3\sqrt{35x}}{10x}= \frac{3\sqrt{35}\sqrt{x}}{10x}[/math].

Now, \(\displaystyle \sqrt{35}= \sqrt{5}\sqrt{7}\) and \(\displaystyle 10= 5(2)\).

\(\displaystyle \frac{\sqrt{5}}{5}= \frac{1}{\sqrt{5}}\) and \(\displaystyle \frac{x}{\sqrt{x}}= \frac{1}{\sqrt{x}}\)
so that can be written \(\displaystyle \frac{3\sqrt{7}}{2\sqrt{5}\sqrt{x}}\).

However, many people prefer a "rationalized denominator" which is exactly the initial form.

Thank you!