Math Help - More problems

1. More problems

Simplify:

$(2 - a^{2}) \cdot \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}}, a > \sqrt {2}$

This one, too:

$x^{n-1} \cdot (x^{n})^{2-n}$

2. Originally Posted by p.numminen
Simplify:

$(2 - a^{2}) \cdot \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}}, a > \sqrt {2}$
$
(2 - a^{2}) \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}}=
(2 - a^{2}) \frac {(a + \sqrt {2})^{1/2}} {(\sqrt {2} + a)^{3/2}}=
(2 - a^{2}) \frac {1} {(\sqrt {2} + a)}=\sqrt{2}-a

$

3. How exactly do you get

$\sqrt{2}-a$ out of $(2 - a^{2}) \frac {1} {(\sqrt {2} + a)}$ ?

4. Hello, p.numminen!

Simplify: . $(2 - a^{2}) \cdot \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}},\;\;a > \sqrt {2}$

We have: . $(2-a^2)\cdot \frac{(\sqrt{2}+a)^{\frac{1}{2}}} {(\sqrt{2}+a)^{\frac{3}{2}}}\;\;=\;\;\frac{2-a^2}{\sqrt{2}+a}$

The numerator factors: . $\frac{(\sqrt{2} - a)(\sqrt{2} + a)}{\sqrt{2} + a}$. . . . . and we can cancel.