Use the product or quotient properties to write each equation in simplified form:
3sqrt{9p^7q^5}

Question

Use the product or quotient properties to write each equation in simplified form:
3sqrt{9p^7q^5}

anonymous · Answer

$$3\sqrt{9p^7q^5}$$

anonymous · Answer

that looks better

anonymous · Answer

$$3\sqrt{9p^7q^5}$$
$$3\sqrt{3^2p^6q^4*pq}$$
$$9p^3q^2\sqrt{pq}$$

In step 2, I separated it into numbers that could be square rooted so I could take it out of the equation.

anonymous · Answer

because the 7 and 5 can not be squared?

anonymous · Answer

Yes. Find the lowest number that can be divided by 2 (because exponent laws say that division means subtraction of exponents and 2 is the index of the radical). In this case, 6 and 4.

anonymous · Answer

*7 and 5 cannot be square rooted to give an integer result.

anonymous · Answer

is it that way for any one that can not be squared?

anonymous · Answer

Yes. Remember for a square root$\sqrt{blah}$, the index is 2. (That's the little number. So it would actually be $$\sqrt[2]{blah}$$

Now we want to square root variables to take them out. You do this by dividing them (technically, it's because square roots can be written as exponents). $x^6$ can be divided by 2 to give $x^3$ (Notice the exponent is being divided). $x^7$ cannot be, so split it up to $x^6 * x$. You can now take out the $x^3$ but NOT the $x$ so leave that inside.

anonymous · Answer

these are so confusing to me, I have a bunch to figure out and a test on it tuesday at noon

anonymous · Answer

If you're willing to learn, I highly recommend the khan academy videos. Specifically: http://www.khanacademy.org/math/algebra/exponents-radicals/v/simplifying-radical-expressions1 http://www.khanacademy.org/math/algebra/exponents-radicals/v/simplifying-radical-expressions-2 http://www.khanacademy.org/math/algebra/exponents-radicals/v/simplifying-radical-expressions-3 Together, it will take you probably about 20-30 minutes to watch, so it's worth a look if you some time tonight.