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
i don't understand what you are trying to say here. can you give an example?
when we raise a number to an exponent, we multiply the exponents.-Exponents like (5^-1)^4 and how to solve them.
so (5^-1)^4 = 5^(-1*4) = 5^-4
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:
-How to use the Pythagorem Theroem properly.
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.
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.-And something called simplifying algebra (this is the thing that I don't get the most)
Example question: (a+b)(2a^2-2b) Simplify.
(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.
same thing here, this is already in a simplified form. let's say we wanted to expand.(3a+5)^2 Simplify.
(3a + 5)^2 = (3a + 5)(3a + 5)
................= 9a^2 + 15a + 15a + 25
................= 9a^2 + 30a + 25
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. Simplify.
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)
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
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 ( ) factor and put it under the square-root. A product of twosquare-roots is the square-root of the product of the two radicands.