Question

Simplifying radicals?

Answer 1

\[\sqrt{\frac{t^2}{t ^{14}}}=\sqrt{\frac{1}{t ^{12}}}=\frac{\sqrt{1}}{\sqrt{t ^{12}}}=\frac{1}{t^6}\]

Answer 2

So what you did was subtract the exponent 2 from top and bottom, how does 1 become one?

Answer 3

how do t become 1 I mean

Answer 4

it is not \(t\) that becomes 1, it is \(t^2\)
think if you had \(\frac{9}{27}=\frac{3^2}{3^3}\) when you cancel the 3's you get \(\frac{1}{3}\)

Answer 5

1/t^6

Answer 6

the 1 is because when you divide, you get a \(1\) left in the numerator

Answer 7

I still don't really understand :/
so we have the equation and then what happens? Why does t^14 become t^12? Am I correct that we subtract the exponent 2 from the top and bottom?

Answer 8

yes

Answer 9

\[\frac{x^{17}}{x^{20}}=\frac{1}{x^3}\]for example

Answer 10

Okay I get that now, so, why does t^12 become t^6?

Answer 11

\[\frac{x^3}{x^5}=\frac{x\times x\times x}{x\times x\times x\times x\times x}=\frac{1}{x^2}\] by cancellation

Answer 12

But we had 1/t^12, what canceled it?

Answer 13

\[\frac{t^2}{t ^{14}}=\frac{t \times t}{t \times t \times t \times t \times t \times t \times t \times t \times t \times t \times t \times t \times t \times t }\]

Answer 14

What is
\[\frac{t}{t}\]

Answer 15

this is the line @Mertsj wrote
\[\sqrt{\frac{t^2}{t ^{14}}}=\sqrt{\frac{1}{t ^{12}}}=\frac{\sqrt{1}}{\sqrt{t ^{12}}}=\frac{1}{t^6}\] the first equal sign is because \(\frac{t^2}{t^{14}}=\frac{1}{t^{12}}\)
the second equal sign is because \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\)
the third equal sign is because \(\sqrt{1}=1\) and \(\sqrt{t^{12}}=t^6\) as \(t^6\times t^6=t^{12}\)

Answer 16

1?

Answer 17

Yes.
\[\frac{t}{t}=\frac{1}{1}\]

Answer 18

So if you do that twice, what do you have in the numerator?

Answer 19

ohh, okay, last question sorry xD What does the square root do? Did it just divide 12 by 2?
Umm you still have 1?

Answer 20

yes

Answer 21

Because extracting the second root is the inverse of raising to the second power. If
\[(t^6)^2=t ^{12}\]

Answer 22

Then
\[\sqrt{t ^{12}}=t^6\]

Answer 23

Extracting the second root?