Simplifying a Radical Expression

**Gatsbro** · August 22nd 2010, 09:36 AM

I have 42+8sqrt2+2sqrt10 over 18. Since it is 42 plus something I am unsure if I am able to reduce 42 to 7 and 18 to 3?? I know I can't simplify any more for the square roots but I was just wondering about the numbers.

**Gatsbro** · August 22nd 2010, 09:49 AM

Simplifying a Radical Expression-possible.jpg

I made a jpg to illustrate what I meant better.

**earboth** · August 22nd 2010, 10:03 AM

Originally Posted by Gatsbro

Click image for larger version.

Name: possible.jpg
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ID: 18682

I made a jpg to illustrate what I meant better.

To simplify a fraction you have to factor the numerator and the denominator. Equal factors can be cancelled because $\dfrac aa = 1~,~a \neq 0$ :

$\dfrac{42+8\sqrt{2}+2\sqrt{10}}{18}=\dfrac{2\left( 21+4\sqrt{2}+\sqrt{10}\right)}{2 \cdot 9}$

... and now it's your turn.

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