Question

need help plz:
simplify:8 times the square root of 63 x to the fifth power

Answer 1

Do you mean:
\[8\sqrt{63x^5} \ or\ 8(\sqrt{63x})^5\]

Answer 2

yes

Answer 3

Which one do you want? The first or the second?

Answer 4

the first

Answer 5

\[8\sqrt{63x^5} = 8\sqrt{9*7x^5} = 8*3\sqrt{7x^5} = 24\sqrt{7x^5}\]
\[=24\sqrt{7x*x^4} = ?\]

What do you think the next step will be?

Answer 6

making x^4 look like x*x*x*x

Answer 7

Your goal is to get x^4 out of the square root? Can you do it as it is, or would it be easier to right x^4 as x^2*x^2?

Answer 8

right x^4 as X^2*X^2

Answer 9

So can you take something out of the square root now?

Answer 10

we can take x^2 out

Answer 11

Bravo! You can get it out as x^4 is x^2*x^2 = (x^2)^2!! So what would you have?

Answer 12

24*2the sqrt of 9*7x

Answer 13

\[24x^2\sqrt{7x}\]

Do you want me to explain this?

Answer 14

yes plz

Answer 15

You can write
\[x^2*x^2 \ as \ (x^2)^2\]
Ok with that?

Answer 16

yes

Answer 17

So what would be the result of:
\[\sqrt{(x^2)^2}\] ?

Answer 18

x^4

Answer 19

Let's try something easier. What is the result of:
\[\sqrt{9}\]?

Answer 20

The result will be a number, that when it's squared, it will produce the number 9. Which number is it?