[SOLVED] Surds

**waven** · March 12th 2009, 07:27 PM

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

thanks

**mathaddict** · March 12th 2009, 07:36 PM

Originally Posted by waven

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

thanks

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

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

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

**waven** · March 12th 2009, 08:12 PM

Originally Posted by mathaddict

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

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

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

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

**mathaddict** · March 12th 2009, 08:43 PM

Originally Posted by waven

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

yes .

note that ab = ba

**waven** · March 12th 2009, 08:47 PM

Originally Posted by mathaddict

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

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

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

btw how did $a^{\frac{3}{2}}$ change to $(a+2)$

**mr fantastic** · March 12th 2009, 09:37 PM

Originally Posted by waven

btw how did $a^{\frac{3}{2}}$ change to $(a+2)$

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

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