Simplify the expressions

1) 2 ^3 sq rt 5 - 4 ^3 sq rt 40 + 3 ^3 sq rt 135

2) sq rt p^7 q^3 - sq rt p^5 q^9 + sq rt p^9 q

3) sq rt b^3 * ^4 sq rt b^3

4) sq rt 16 - 8x + x^2

I am completely lost I try researching everything for help I can only do some of the problems half way and get stuck.

2. Originally Posted by Sammyj
1) 2 ^3 sq rt 5 - 4 ^3 sq rt 40 + 3 ^3 sq rt 135
If I am reading this correctly:
$2 \sqrt[3]{5} - 4 \sqrt[3]{40} + 3 \sqrt[3]{135}$

$= 2 \sqrt[3]{5} - 4 \sqrt[3]{2^3 \cdot 5} + 3 \sqrt[3]{3^3 \cdot 5}$

$= 2 \sqrt[3]{5} - 4 \cdot 2 \sqrt[3]{5} + 3 \cdot 3 \sqrt[3]{5}$

$= 2 \sqrt[3]{5} - 8 \sqrt[3]{5} + 9 \sqrt[3]{5}$

$= 3 \sqrt[3]{5}$

The key to simplifying $\sqrt[n]{x}$ is to find factors of x that are
powers of n. Such as the case of $\sqrt[3]{135}$: I knew to look for a factor of the form $a^3$, and by looking I found that $135 = 5 \cdot 27 = 5 \cdot 3^3$. Then you can bring that number outside the radical.

Try the other ones again. If you get stuck, post your solution and we'll see where things went sour.

-Dan

3. Thanks a lot! This was very helpful