Question

help please (:
fan and medal <3


1. what is the simplest form of the radical expression?

sqrt2 + sqrt5 / sqrt2 - sqrt5

2. write (8a^-3)^ -2/3 in simplest form

Answer 1

The first one:
Start by making common denominators (ie multiply the other two fractions by sqrt2 on the top and bottom). Then combine them together and multiply that fraction by sqrt2 on the top and bottom. You can then factor out a (1/2) to get:
\[(1/2)(2\sqrt2+\sqrt10-2\sqrt5)\]

Answer 2

Yep.

Answer 3

Second one:
The answer is \[\frac{ 1 }{ 4 }x^2\] Want me to explain that?

Answer 4

Ok. x^2 comes from the power rule:
\[(x^a)^b=x^{ab}\]
Basically if a power is in a bracket and it's to another power, you multiply the two together.
You still have to take care of the 8, which is simply \[8^{-\frac{ 2 }{ 3 }}\] I stuck that in a calculator because that's nasty, which punches out a number of (1/4).

Answer 5

For sure! If you multiply the other two fractions by sqrt2, you get:
\[\frac{ \sqrt2\sqrt2 }{ \sqrt2 }+\frac{ \sqrt5}{ \sqrt2 }-\frac{ \sqrt2\sqrt5 }{ \sqrt2 }\]
Combine and simplify to:\[\frac{ 2+\sqrt5-\sqrt{10} }{ \sqrt2 }\]
Now multiply the top and bottom by sqrt2:
\[\frac{ 2\sqrt2+\sqrt{10}-\sqrt{20}}{2}\]
Now you can factor out the 2 on the bottom as (1/2) in front AND simplify sqrt20 to 2sqrt5:\[\sqrt{20}=\sqrt{5*4}=2\sqrt5\]
\[(1/2)(2\sqrt2+\sqrt{10}-2\sqrt5)\]Does this help?