# Explanations

• May 11th 2007, 08:50 PM
Rocher
Explanations
I would just like to know how to do the following things:

-Change radicals from whole to mixed and vice/versa.

-Exponents like (5^-1)^4 and how to solve them.

-How to use the Pythagorem Theroem properly.

-And something called simplifying algebra (this is the thing that I don't get the most)
Example question: (a+b)(2a^2-2b) Simplify.
(3a+5)^2 Simplify.
2(a^-3)^2+3(b^2)^-2. Simplify.

Hopefully you guys could help me understand this stuff :P
• May 11th 2007, 08:56 PM
qbkr21
Re
Quote:

Originally Posted by Rocher
-Change radicals from whole to mixed and vice/versa.

What do you mean by this?
• May 11th 2007, 09:04 PM
Rocher
Got it.

http://i3.tinypic.com/4lxf5tj.jpg

Would be an example from whole radical to mixed. I have no idea how to get mixed to whole though.
• May 11th 2007, 09:05 PM
qbkr21
Re
Quote:

Originally Posted by Rocher
I would just like to know how to do the following things:
-Exponents like (5^-1)^4 and how to solve them.

RE:
• May 11th 2007, 09:10 PM
Rocher
Ooh, thanks I get that now! :D
• May 11th 2007, 09:10 PM
Jhevon
Quote:

Originally Posted by Rocher
I would just like to know how to do the following things:

-Change radicals from whole to mixed and vice/versa.

i don't understand what you are trying to say here. can you give an example?

Quote:

-Exponents like (5^-1)^4 and how to solve them.
when we raise a number to an exponent, we multiply the exponents.

so (5^-1)^4 = 5^(-1*4) = 5^-4

Quote:

-How to use the Pythagorem Theroem properly.
for a right angled triangle in which the length of the legs of the triangle are a and b and the length of the hypotenuse (the longest side) is c, we have by Pythagoras' theorem:

a^2 + b^2 = c^2

there is no fancy way to use this properly. you just solve for what you want, generally you will have only one of the letters unknown in the equation.

Quote:

-And something called simplifying algebra (this is the thing that I don't get the most)
Example question: (a+b)(2a^2-2b) Simplify.
i'd say this is simplified, but i guess you want me to expand. when we are expanding two or more sets of brackets, we peform the following procedure. we the the first term from the first set of brackets and multiply everything in the second set of brackets, then we take the second term in the first set of brackets and multiply everything in the second set and so on. then we add (or subtract) accordingly. for more than two sets of brackets, we do it two at a time.

(a + b)(2a^2 - 2b) = 2a*a^2 - 2a*b + 2b*a^2 - 2b*b
..........................= 2a^3 - 2ab + 2ba^2 - 2b^2
So yeah, like i said, this isn't really simplifying. simplifying would be to go from the last line i typed to the line you gave me.

Quote:

(3a+5)^2 Simplify.
same thing here, this is already in a simplified form. let's say we wanted to expand.

(3a + 5)^2 = (3a + 5)(3a + 5)
................= 9a^2 + 15a + 15a + 25
................= 9a^2 + 30a + 25

Quote:

2(a^-3)^2+3(b^2)^-2. Simplify.
so, as i said before, when we raise a number to a power, we multiply the powers.

2(a^-3)^2 + 3(b^2)^-2 = 2a^(-3*2) + 3b^(2*-2)
..................................= 2a^-6 + 3b^-4
Now negative powers mean we take the inverse, THEY DO NOT CHANGE THE SIGN OF A NUMBER, so if you are so inclined, we can simplify this a bit further as follows.

= 2(1/a^6) + 3(1/b^4) ...............since x^-a = 1/(x^a)
= 2/(a^6) + 3/(b^4)
• May 11th 2007, 09:13 PM
qbkr21
Re:

Convert to a decimal then square it. Try and see if this works...

-qbkr21
• May 11th 2007, 09:16 PM
Rocher
I did give you an example of radicals. Look up! And thanks for the other stuff :)
• May 11th 2007, 09:17 PM
Jhevon
Quote:

Originally Posted by Rocher
I did give you an example of radicals. Look up! And thanks for the other stuff :)

ok, i see it now, but qbkr21 seemed to have addressed the problem already. i'll leave the rest to him
• May 11th 2007, 09:19 PM
Rocher
Quote:

Originally Posted by qbkr21

Convert to a decimal then square it. Try and see if this works...

-qbkr21

How do you convert it into a decimal exactly?
• May 11th 2007, 09:24 PM
qbkr21
Re:
• May 11th 2007, 09:28 PM
Rocher
Oh alright.
http://i10.tinypic.com/6as8g1y.jpg

Is that right?
• May 11th 2007, 09:33 PM
qbkr21
Re:
No!

In fact the square root of 400, is a perfect square. Why?

Because

20*20=400

The method we talked about should be your second choice

First see if anything will multiply by itself and go into it evenly if not then use the method we discussed.

-qbkr21
• May 11th 2007, 09:36 PM
Rocher
Oh... **** lolz... must be getting too tired =). Well thank you both for helping me :).
• May 12th 2007, 12:37 AM
earboth
Quote:

Originally Posted by Rocher
I would just like to know how to do the following things:

-Change radicals from whole to mixed and vice/versa.

....

Hi,

how to change a radical into mixed notation was demonstrated in the previous posts.

Sometimes (especially in calculus) it is convenient to transform a radical in mixed notation into a whole radical.

Example:

5*sqrt(5) = sqrt(25) * sqrt(5) = sqrt(25 * 5) = sqrt(125)

Method: square the non-radical (:D ) factor and put it under the square-root. A product of twosquare-roots is the square-root of the product of the two radicands.