Question

Can i get some help on this please? i need to find out how to do this... (radicals)

Answer 1

What is \(\sqrt{3^4} \) ?

Answer 2

9?

Answer 3

i think..

Answer 4

Correct, but notice the following:
\( \sqrt{3^4} = \sqrt{81} = 9 = 3^2\)
Ok?

Answer 5

Okay o:

Answer 6

Now let's go from the fisrt step to the last, skipping all the middle steps.

\(\sqrt{3^4} = 3^2\)

Similary,

\( \sqrt{5^8} = 5^4 \)

\(\sqrt{x^{20}} = x^{10}\)

You see what happens to the exponent when you take the square root?

Answer 7

So the exponents turn into only half of what the were?

Answer 8

Right. That's what taking the square root does.
Now let's look at your example.
Your exponent is 13, so half would be 6.5.
Your problem is not looking for a decimal exoponent.
Instead it's looking for this.

Answer 9

\( \sqrt{x^{13}} = \sqrt{x^{12} \cdot x} = \sqrt{x^{12}} \sqrt{x} \)

You know how to simplify \(\sqrt{x^{12}} \) since you know that the exponent will become half when you take the square root.

The part \(\sqrt{x} \) just remains like that since if you divide the exponent 1 by 2 you get 0.5, which is not what we want.

Answer 10

This is why we can separate x^13 into x^12 * x:

\(x^{13} = x^{12 + 1} = x^{12} \cdot x^1 = x^{12} \cdot x\)

Answer 11

Oohh okay, this makes sense to me, it's just always gonna me confusing to me... Radicals just aren't my thing

Answer 12

Great.

Answer 13

Does x^12 simplify to x^6?

Answer 14

Not x^12, the square root of x^12 is x^6

Answer 15

square root of x is equal to the x^1/2

Answer 16

if you know what i mean

Answer 17

Okay

Answer 18

\( x^{12} = x^6 \cdot x^6 \)

\( \sqrt{x^{12}} = x^6 \)

Answer 19

ohh okay, thanks ^-^

Answer 20

wlcm