## AngelaB97 one year ago how do you solve this radical problem

1. AngelaB97

|dw:1441681695839:dw|

2. AngelaB97

in thorough steps cuz i don't seem to understand this

3. anonymous

So you will need to simplify each radical and then multiply them together. Let's start with the first one. We know that 2^3 is 8 and 3^3 is 27, so it only follows that the cube root of 15 must be in between 2 and 3 as 15 is between 8 and 27 and the opposite of an exponent is a root. But where is it between 2 and 3? Well, to figure that out we must approximate. But that is a very long process. So instead, let's go through the first-decimal-digit possibilities. Let's start with ones closer to 2 as 8 is closer to 15. $2.2^{3}=10.648$ Not quite. $2.4^{3}=13.824$ Closer... let's try one more. $2.5^{3}=15.625$ That's a bit too far. So we know it must be a bit smaller than 2.5 but quite a bit bigger than 2.4 You could keep repeating this process until you get it perfect, but I quite honestly do not feel like it. So I plugged it into my calculator and get approximately 2.466 Now for the next one. Cube root of 75. Well, 8^3=64 and 9^3=81, so it must be between 8 and 9. You could repeat the process above, but the calculator informs me it is about 4.217 Now for the easy part! $2.466\times4.217=10.399$

4. AngelaB97

but its still supposed to be in radical form not decimal

5. anonymous

Ah... that's different.

6. AngelaB97

can you explain in that way?

7. anonymous

I shall try =)

8. anonymous

Find the prime factorization of both numbers |dw:1441682872453:dw|

9. anonymous

You're taking a cube root, so look for group of 3 numbers|dw:1441683029075:dw|

10. anonymous

Going off of what peachpi said, then you can multiply those under the cube root$\sqrt[3]{5\times3\times5\times5\times3}$ and then see that there are 3 5's. Because it is a cube root, only one 5 can stay, and we pull it out of the cube root, so we are left with $5\sqrt[3]{3\times3}$

11. anonymous

Write the grouped number on the outside of the radical, multiply the numbers left in the radical|dw:1441683084511:dw|

12. anonymous

There you go!!

13. AngelaB97

doesn't the rad 9 come out of the square root

14. anonymous

No. Because it is a cube root and not a square root. 2^3 is only 8, while 3^3 is 27. This is the simplest you will be able to get in radical form =)

15. AngelaB97

16. anonymous

Sure =)

17. AngelaB97

|dw:1441683413491:dw|

18. anonymous

You'll need to do something similar here, but I have not learned how to find roots of fractions yet. I could do it in decimal form, but I know that's not what you need. I'm very sorry!!

19. AngelaB97

it's fine thanks for your help!

20. anonymous

No problem =)