Question

Which expression is the simplified form of sqrt r^49

Answer 1

7

Answer 2

is it \[r^7 \sqrt{r}\]

Answer 3

In general

\[\Large \sqrt{x^k} = x^{\frac{k}{2}}\]

if k is even


OR

\[\Large \sqrt{x^k} = x^{\frac{k-1}{2}}\sqrt{x}\]

if k is odd

Answer 4

wait that confused me a lil

Answer 5

where are you stuck

Answer 6

the k/2 part

Answer 7

Here are 2 examples:

Even Example: If k = 8, then

\[\Large \sqrt{x^k} = x^{\frac{k}{2}}\]

\[\Large \sqrt{x^8} = x^{\frac{8}{2}}\]

\[\Large \sqrt{x^8} = x^{4}\]


Odd Example: If k = 13, then

\[\Large \sqrt{x^k} = x^{\frac{k-1}{2}}\sqrt{x}\]

\[\Large \sqrt{x^{13}} = x^{\frac{13-1}{2}}\sqrt{x}\]

\[\Large \sqrt{x^{13}} = x^{\frac{12}{2}}\sqrt{x}\]

\[\Large \sqrt{x^{13}} = x^{6}\sqrt{x}\]

Answer 8

The k/2 means take whatever number k is and cut it in half

Answer 9

Like the example above shows

Answer 10

o ok i see