# [SOLVED] Surds

• Mar 12th 2009, 07:27 PM
waven
[SOLVED] Surds
Q. simpify: $\displaystyle \sqrt a^3 + 2 \sqrt a$
the answer is $\displaystyle (a+2)\sqrt a$ but but i can't seem to figure out the solution.

thanks
• Mar 12th 2009, 07:36 PM
Quote:

Originally Posted by waven
Q. simpify: $\displaystyle \sqrt a^3 + 2 \sqrt a$
the answer is $\displaystyle (a+2)\sqrt a$ but but i can't seem to figure out the solution.

thanks

$\displaystyle a^{\frac{3}{2}}+2a^{\frac{1}{2}}$

Take out the common factor which is $\displaystyle a^{\frac{1}{2}}$

$\displaystyle a^{\frac{1}{2}}(a+2)$ which is similar the ans given.
• Mar 12th 2009, 08:12 PM
waven
Quote:

$\displaystyle a^{\frac{3}{2}}+2a^{\frac{1}{2}}$

Take out the common factor which is $\displaystyle a^{\frac{1}{2}}$

$\displaystyle a^{\frac{1}{2}}(a+2)$ which is similar the ans given.

is $\displaystyle a^{\frac{1}{2}}$ the common factor because there are 2 $\displaystyle a^{\frac{1}{2}}$s?
and
would it still be the same answer it it was $\displaystyle \sqrt a(a+2)$ rather than $\displaystyle (a+2)\sqrt a$
• Mar 12th 2009, 08:43 PM
Quote:

Originally Posted by waven
is $\displaystyle a^{\frac{1}{2}}$ the common factor because there are 2 $\displaystyle a^{\frac{1}{2}}$s?
and
would it still be the same answer it it was $\displaystyle \sqrt a(a+2)$ rather than $\displaystyle (a+2)\sqrt a$

yes .

note that ab = ba
• Mar 12th 2009, 08:47 PM
waven
Quote:

$\displaystyle a^{\frac{3}{2}}+2a^{\frac{1}{2}}$

Take out the common factor which is $\displaystyle a^{\frac{1}{2}}$

$\displaystyle a^{\frac{1}{2}}(a+2)$ which is similar the ans given.

btw how did $\displaystyle a^{\frac{3}{2}}$ change to $\displaystyle (a+2)$
• Mar 12th 2009, 09:37 PM
mr fantastic
Quote:

Originally Posted by waven
btw how did $\displaystyle a^{\frac{3}{2}}$ change to $\displaystyle (a+2)$

$\displaystyle a^{\frac{3}{2}} = a^{1 + \frac{1}{2}} = a \cdot a^{\frac{1}{2}}$.