Problem with Root

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November 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
November 17th 2009, 01:55 AM
Grandad

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: $\sqrt{a}\times\sqrt{a} = a$ ...Rule 1

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

So, using these rules, we can say:
$3\sqrt2 =\sqrt3\sqrt3\sqrt2$ , using Rule 1
$=\sqrt{3\times3\times2}$ , using Rule 2, twice

$=\sqrt{18}$

Here are another couple of examples:

(1) $5\sqrt3=\sqrt5\sqrt5\sqrt3$
$=\sqrt{5\times5\times3}$

$=\sqrt{75}$

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

$=3\sqrt2$

$=\sqrt{18}$

Grandad
November 17th 2009, 03:27 AM
HallsofIvy

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

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

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