Surds: i really really need help!!!

[kt01]

1: (3√7)^2

2: (8+√5)(2-√5)

3: Given that 32√2=2^a , find the value of 'a'

4: Write down the value of 125^ 1/3

5: Find the value of 125 ^-2/3

6: Expand and simplify (√7 +2)(√7-2)

7: Factorise completely: x^3 - 9x

8: Find the value of 8 ^4/3

9: Simplify
15x^4/3
---------
3x

10: Express √108 in the form a √3, where a is an integer.

11: solve the equation: 2^1-x =4^x

 

[stapel]

Please reply showing your work so far, or else specify that you are requesting lesson instruction first. Thank you! :wink:

 

[kt01]

Are you a student attending math classes?
If so, was the teacher absent?

I do homestudy and i really need these answers... doesnt matter what the working is... thank you

 

[JeffM]

I do homestudy and i really need these answers... doesnt matter what the working is... thank you

Ahh, but it does matters to us what the working is. And it SHOULD matter to you BECAUSE, if you do not know the working, how will you be able to pass your test?

Here is the basic thing to remember: surds are just numbers. Here is the definition:

\(\displaystyle a = \sqrt[n]{b}\ MEANS\ a^n = b\ and\ vice\ versa.\)

Here is an example worked out for you:

\(\displaystyle Simplify\ if\ possible\ 3\sqrt[5]{32}.\)

If it is possible to simplify that expression, that means there is a simple number that when multiplied by itself five times = 32.

You can use a decent calculator to get the answer, but suppose you do not have one handy.

It should be obvious that the number is bigger than 1 because 1 * 1 * 1 * 1 * 1 = 1. It must be smaller than 6 because 6 * 6 = 36 > 32.
It must be smaller than 5 because 5 * 5 * 5 = 125 > 32. It must be smaller than 4 because 4 * 4 * 4 = 64 > 32. It must be smaller than
3 because 3 * 3 * 3 * 3 = 81 > 32. That leaves 2 to try. 2 * 2 * 2 * 2 * 2 = 4 * 2 * 2 * 2 = 8 * 2 * 2 = 16 * 2 = 32.

\(\displaystyle So\ \sqrt[5]{32} = 2 \implies 3\sqrt[5]{32} = 3 * 2 = 6.\)

Now try working out your problems. You can ask us to check your work if you show it. Alternatively, you can ask us to confirm your answers, but in that case we cannot tell you where you made any mistakes.

 

[JeffM]

...ran short of blue ink?

Precisely. I write backwards you see.

 

[kt01]

I fully understand what you are saying,

I just find it easier to work backwards and understand it from there, thats my point!

Thanks for the help though and its not a test btw its just extra work i wanted to do because i didn't understand it.

Do you think you could help with the questions?

Ahh, but it does matters to us what the working is. And it SHOULD matter to you BECAUSE, if you do not know the working, how will you be able to pass your test?

Here is the basic thing to remember: surds are just numbers. Here is the definition:

\(\displaystyle a = \sqrt[n]{b}\ MEANS\ a^n = b\ and\ vice\ versa.\)

Here is an example worked out for you:

\(\displaystyle Simplify\ if\ possible\ 3\sqrt[5]{32}.\)

If it is possible to simplify that expression, that means there is a simple number that when multiplied by itself five times = 32.

You can use a decent calculator to get the answer, but suppose you do not have one handy.

It should be obvious that the number is bigger than 1 because 1 * 1 * 1 * 1 * 1 = 1. It must be smaller than 6 because 6 * 6 = 36 > 32.
It must be smaller than 5 because 5 * 5 * 5 = 125 > 32. It must be smaller than 4 because 4 * 4 * 4 = 64 > 32. It must be smaller than
3 because 3 * 3 * 3 * 3 = 81 > 32. That leaves 2 to try. 2 * 2 * 2 * 2 * 2 = 4 * 2 * 2 * 2 = 8 * 2 * 2 = 16 * 2 = 32.

\(\displaystyle So\ \sqrt[5]{32} = 2 \implies 3\sqrt[5]{32} = 3 * 2 = 6.\)

Now try working out your problems. You can ask us to check your work if you show it. Alternatively, you can ask us to confirm your answers, but in that case we cannot tell you where you made any mistakes.

 

[JeffM]

I fully understand what you are saying,

I just find it easier to work backwards and understand it from there, thats my point!

Thanks for the help though and its not a test btw its just extra work i wanted to do because i didn't understand it.

Do you think you could help with the questions?

Sure. That is what we are here for (even including Denis). I did not think THIS was a test. I was just saying that if we give answers, you don't learn anything that will help you on a test. It's good to do extra work to understand.

Some guidance on how best to use this site.

Post one problem per thread. Make sure the problem is stated clearly.

If you just tell us what answer you get to a problem on your own, we shall tell you whether it is right or not.

If you show us an answer plus your work or as much work as you can do on your own, we can tell you where you made a mistake (if you did) or help you get past your difficulty. So I suggest you use this thread to work the first problem, asking for help when and where you need it. Then start another thread for the next problem, and so on.

OK?