Thread: Please Help

I have to learn how do roots without a calculator and one of the practice problems i get was 12 root of 64 equal square root of two.How could i figure out problems like these without a calculator?Also what is (n^3m^9)^1/2?

Originally Posted by anime_maniac20

I have to learn how do roots without a calculator and one of the practice problems i get was 12 root of 64 equal square root of two.

Start by factoring 64 down to it's prime factorization,


So 64 can be written as

Keep this in mind.

So by the definition of roots,

Now substituting the prime factorization of 64 in place of 64, and writing it as an exponent as previously shown we get,



Using the law for the power of a power, we multiply the exponents together which gives us,

Also what is (n^3m^9)^1/2?

Using the same law of exponents the outside exponent gets "distributed" to each inside term.



Or we can also do it this way,



These are all equivalent statements.

Using the same law of exponents the outside exponent gets "distributed" to each inside term.



Or we can also do it this way,

I had the exact answers but the answer that was correct was like

Originally Posted by anime_maniac20

I had the exact answers but the answer that was correct was like

Ah...

That is correct, there was one step of simplification that I missed, thank you.

We can further simplify this by,





I skipped a few steps there where I used the rules I previously discussed. Let me know if you follow this o.k.

Thank you so much,I did understand it. You mad it look really simple.