Question

square root to the 3rd power n^2 -1+4 =3

Answer 1

\[\sqrt[3]{n ^{2}-1}+4=3?\]

Answer 2

\[\sqrt[3]{n^2 -1+4}=3\]

Answer 3

yes.

Answer 4

cool. Cube both sides first.

Answer 5

Wait. Which equation? Yours or mine?

Answer 6

they're the same.

Answer 7

could give me a visual of cubing both sides.

Answer 8

Mine has the +4 on the outside of the root. Yours has it on the inside. Which one is it?

Answer 9

If it's on the outside, then you'll subtract 4 first.
If it's on the inside, then you'll cube both sides first.

Answer 10

yours

Answer 11

Okay. So subtract 4 first and you'll get...\[\sqrt[3]{n ^{2}-1}=-1\]

Answer 12

Then cube both sides and you'll get...\[n ^{2}-1=-1\]

Answer 13

okay.

Answer 14

Next, add 1 to both sides and you'll get...\[n ^{2}=0\]

Answer 15

Therefore, n = 0.

Answer 16

Which if you plug it into the original equation, it works. You can take the cube root of negative numbers, but you can't take the square root. As a matter of fact:
You can take the ODD-number root of any negative number.
But you CANNOT take the EVEN-number root of any negative number.
Just a rule to keep in mind.
Take care.

Answer 17

thank you.