# Problem with Root

• Nov 16th 2009, 08:03 PM
hovermet
Problem with Root
I don't understand how 3√2 = to √18.. and how to get rid of the root to become 3 x 2. Can anyone show me a few more examples also?

Thank You
• Nov 17th 2009, 01:55 AM
Hello hovermet
Quote:

Originally Posted by hovermet
I don't understand how 3√2 = to √18.. and how to get rid of the root to become 3 x 2. Can anyone show me a few more examples also?

Thank You

Two things you need to know about square roots:
The definition of a square root: $\displaystyle \sqrt{a}\times\sqrt{a} = a$ ...Rule 1

How multiplication works with square roots: $\displaystyle \sqrt{a}\times\sqrt{b} = \sqrt{ab}$ ...Rule 2
So, using these rules, we can say:
$\displaystyle 3\sqrt2 =\sqrt3\sqrt3\sqrt2$, using Rule 1
$\displaystyle =\sqrt{3\times3\times2}$, using Rule 2, twice

$\displaystyle =\sqrt{18}$
Here are another couple of examples:
(1) $\displaystyle 5\sqrt3=\sqrt5\sqrt5\sqrt3$
$\displaystyle =\sqrt{5\times5\times3}$

$\displaystyle =\sqrt{75}$
(2) $\displaystyle \sqrt8 + \sqrt2 = \sqrt{2\times2\times2} + \sqrt2$
$\displaystyle =2\sqrt2+1\sqrt2$

$\displaystyle =3\sqrt2$

$\displaystyle =\sqrt{18}$
$\displaystyle 3\sqrt{2}= \sqrt{3^2}\sqrt{2}= \sqrt{9}\sqrt{2}= \sqrt{9(2)}= \sqrt{18}$. I don't know what you mean by "get rid of the root to become 3 x 2". You can't- $\displaystyle 3\sqrt{2}$ and 3x2 are not equal and you can't just "make" them equal.