## vivalakoda 2 years ago Subtracting radicals?

1. vivalakoda

$\left( 7-√54 \right) - \left( 5+√24 \right)$

2. Galice

You can split each radical up like so: $\sqrt{54} = \sqrt{6 \times 9}$ You can also perform the same for the other radical: $\sqrt{24} = \sqrt{6 \times 4}$ Once you've done that, you can pull out any perfect squares that you have found. In this case, you've just found 9 and 4, which root down to 3 and 2, respectively. Now you have: $\left( 7- 3\sqrt{6} \right) - \left( 5 + 2\sqrt{6} \right)$ Does that help?

3. vivalakoda

I've gotten as far as that, simplifying the radicals. But I'm confused as to how to go about the subtracting with a subtraction problem within a subtraction problem

4. waterineyes

Distribute -1 to the brackets..

5. waterineyes

$-1(5+2 \sqrt{6}) = ??$

6. vivalakoda

= -5-2√6

7. waterineyes

Yep..

8. waterineyes

Now: $7- 3\sqrt{6} - 5 - 2\sqrt{6} = ??$

9. vivalakoda

2-5√6? D:

10. waterineyes

Then where is the problem?? Yes, well done...

11. vivalakoda

I guess I just needed a walkthrough. Hah thanks!