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

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- Nov 16th 2009, 08:03 PMhovermetProblem 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 AMGrandad
Hello hovermetTwo things you need to know about square roots:

The definition of a square root: $\displaystyle \sqrt{a}\times\sqrt{a} = a$ ...Rule 1So, using these rules, we can say:

How multiplication works with square roots: $\displaystyle \sqrt{a}\times\sqrt{b} = \sqrt{ab}$ ...Rule 2

$\displaystyle 3\sqrt2 =\sqrt3\sqrt3\sqrt2$, using Rule 1Here are another couple of examples:$\displaystyle =\sqrt{3\times3\times2}$, using Rule 2, twice

$\displaystyle =\sqrt{18}$

(1) $\displaystyle 5\sqrt3=\sqrt5\sqrt5\sqrt3$Grandad$\displaystyle =\sqrt{5\times5\times3}$(2) $\displaystyle \sqrt8 + \sqrt2 = \sqrt{2\times2\times2} + \sqrt2$

$\displaystyle =\sqrt{75}$

$\displaystyle =2\sqrt2+1\sqrt2$

$\displaystyle =3\sqrt2$

$\displaystyle =\sqrt{18}$

- Nov 17th 2009, 03:27 AMHallsofIvy