Hello hovermet 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$
$\displaystyle =3\sqrt2$
$\displaystyle =\sqrt{18}$
Grandad