Question

how do i solve 256=r^4

Answer 1

Find the fourth root of both sides:

\[\sqrt[4]{256} = \sqrt[4]{r}^{4}\]

The fourth root of 256 is 4, therefore r = 4

Answer 2

is there a calculator function for that?

Answer 3

or should i just guess to find answer?

Answer 4

There should be, but you could also put it to the power of 1/4, for example:
\[256^{1/4}\]

Answer 5

Some calculators have it, and others do not - but putting the answer to the power to 1/4 should always work.

If you were finding a fifth root, you could do the same thing, except you would use the power of 1/5.

Answer 6

i see when i type it in i get 64 though

Answer 7

is my calculator being weird? your math makes sense

Answer 8

never mind i figured it out. thank you though

Answer 9

You could try this calculator:
http://web2.0calc.com/

I just used it and it gave me 4. Make sure you're using the exponent button and not accidentally hitting anything else

Answer 10

No problem!

Answer 11

for anyone who has a ti-83 plus and has a simmilar problem
Example: Find the 5th root of 16807.

• Input 5.
• Press [MATH] [5] to input the nth root command.
• Input 16807 and press [ENTER] to complete the calculation.

Answer 12

looks the possibly other is -4
(-4)^4 = 256 (correct too)

Answer 13

r^4 = 256
r^4 - 256 = 0
(r^2)^2 - 16^2 = 0
(r^2 + 16)(r^2 - 16) = 0
r^2 + 16 = 0 (no roots are real)
r^2 - 16 = 0
(r+4)(r-4) = 0
the real roots satisfied for
r = 4 or r = -4