square root of 360x^12

Question

jtug6 · Answer

What would be the square root of 360? Do you know?

jtug6 · Answer

Or the simplified form of it i should say

anonymous · Answer

no i dont

jtug6 · Answer

Ok well actually i was misleading you. 360 isn't a perfect square so if you take it's square root you won't get a whole number. However, we can find the highest perfect square that when multiplied with a non-perfect square gives us 360.

anonymous · Answer

$$\sqrt{360x ^{12}}$$

jtug6 · Answer

Yep. So lets break it apart. 360 is 10*36 right?

jtug6 · Answer

So, is 10 or 36 a perfect square?

anonymous · Answer

36

jtug6 · Answer

mhm. so then whats the square root of that?

anonymous · Answer

6

jtug6 · Answer

okay so now we yank it out of the radical so it becomes $$6\sqrt{10x ^{12}}$$

jtug6 · Answer

now then, hmmm. x is being raised to a power of 12, right?

anonymous · Answer

so is that the answer

jtug6 · Answer

not yet. we're dealing with x^12 still

jtug6 · Answer

its being raised to 12 and it's underneath the radical which is a special case. we actually divide the 12 by 2 to get 6 so what would happen then?

jtug6 · Answer

the reason why is because the square root is a power to one half so if we say (x^12)^1/2 we would know from the exponent rules that we would multiply in this case. so 12*1/2 is 6. :P

jtug6 · Answer

so the square root got rid of 36 and x^12 and made it 6 and x^2. What should it's final form look like?