Question

Express the following in simplest radical form. All variables represent positive real numbers.
5/7 square24xy^5
Please break down the steps for me.

Answer 1

\[\frac{ 5 }{ 7 }\sqrt{24xy^5}\]

Answer 2

the \(\frac{5}{7}\) out front you can ignore until the end
you need to worry about the \(24\) inside the radical, and also the \(y^5\)

Answer 3

okay

Answer 4

\[\sqrt{24}\] is not in simplest radical form because \(24=4\times 6\) making
\[\sqrt{24}=\sqrt{4\times 6}=\sqrt{4}\times \sqrt{6}=2\sqrt{6}\]
you don't need to write all those steps, that was just by explanation

Answer 5

\[\sqrt{y^5}\] is not in simplest radical form because the power is 5, which is larger than the index which is 2 (square root)
so
\[\sqrt{y^5}=\sqrt{y^2\times y^2\times y}=\sqrt{y^2}\times \sqrt{y^2}\times \sqrt{y}\]
\[=y\times y\times \sqrt{y}=y^2\sqrt{y}\] again all steps are not necessary, just for explanation

Answer 6

the snap way to do that one is to say that two goes in to five twice, with a remainder of 1, so that
\[\sqrt{y^5}=y^2\sqrt{y}\] i.e. two \(y\)'s come out and one stays in

Answer 7

wow, this problem is hard but thank you for explaning it to me

Answer 8

so a "final answer" is
\[\frac{5}{7}\times 2\times y^2\sqrt{xy}\] or
\[\frac{10y^2}{7}\sqrt{xy}\]

Answer 9

no i made a mistake, final answer is
\[\frac{10y^2}{7}\sqrt{6xy}\]

Answer 10

it is not that hard with a little practice
for example
\[\sqrt{x^9}\] is
\[x^4\sqrt{x}\] because 2 goes in to 9 4 times, with a remainder of 1 so 4 come out, one stays in

Answer 11

oh okay, i kind of getting it

Answer 12

works with larger indexes as well
\[\sqrt[3]{x^{11}}=x^3\sqrt{x^2}\]because 3 goes in to 11 3 times with a remainder of 2, so three come out, two stay in

Answer 13

also
\[\sqrt{50}=5\sqrt{2}\] because \(50=25\times 2\) and the square root of 25 you know is 5

Answer 14

Again, thanks