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?

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- Apr 22nd 2008, 04:00 PM #1

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- Apr 22nd 2008, 04:57 PM #2
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.

- Apr 22nd 2008, 07:09 PM #3

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- Apr 22nd 2008, 07:24 PM #4

- Apr 22nd 2008, 08:08 PM #5

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