?25t^11 Simplify the radical?

Are you taking a class? What have you learned, so far?

There's more than one way to simplify radicals.

Here's one way of thinking about it:

\(\displaystyle \sqrt{25 \cdot t^{11}}\)

\(\displaystyle \sqrt{5^2 \cdot t^{10} \cdot t}\)

\(\displaystyle \sqrt{5^2} \cdot \sqrt{t^{10}} \cdot \sqrt{t}\)

\(\displaystyle 5 \cdot t^5 \cdot \sqrt{t}\)

Here's another way to do it (switch from radical form to exponential form):

\(\displaystyle (25 \cdot t^{11})^{1/2}\)

\(\displaystyle 25^{1/2} \cdot t^{11/2}\)

\(\displaystyle 5 \cdot t^{10/2} \cdot t^{1/2}\)

\(\displaystyle 5 \cdot t^5 \cdot \sqrt{t}\)
 
Thank you. I have not learned the exponential form route that you took. But the first one is familiar. I'm taking beginning algebra right now. I have learned what you are explaining, but sometimes forget what to do and just need a little guidance.
 
Okay. When simplifying square roots, you basically want to look for squared factors in the radicand. Each pair of twin factors in the radicand becomes a single factor "out in front". With practice, you'll take short-cuts.

\(\displaystyle \sqrt{5^2 \cdot t^2 \cdot t^2 \cdot t^2 \cdot t^2 \cdot t^2 \cdot t} = 5 \cdot t \cdot t \cdot t \cdot t \cdot t \cdot \sqrt{t}\)

If you use Windows, the character map has some mathematical symbols:

?(25t^11)

I used LaTex commands above. Click the quote button on any post containing LaTex, to see the commands.
 
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