Question

solve
( w - 3) ^3 = 16

Answer 1

@Nurali @Hero @mathstudent55

Answer 2

with order of operations, you can first take out the exponent from the parenthesis area

Answer 3

ik that can u pls do it so I can see how u did it

my answer is wrong

Answer 4

@atlas

Answer 5

w - 3 = 16^(1/3)
w = 16^(1/3) + 3

Answer 6

hkim is right

Answer 7

let me clarify real quick with the last part
w = [16^(1/3)] + 3

Answer 8

if two sides are equal you can perform the same operation on both sides without changing the equality - right?

Answer 9

so we take cube root on both sides to get:
w-3 = 16^(1/3)

Answer 10

yh I know but hits confusing to find 16^1/3 without calculator. can u tell me how to do it if u know

Answer 11

now you can find w = 3 + 16^(1/3)
I added 3 on both sides

Answer 12

it is an irrational sum... 16^(1/4) would be easy but 16^(1/3) isn't

Answer 13

but im not suppose to use calculator as im instructed by my teacher

Answer 14

normally we factorize the number and group the similar factors into pairs of 3.......but here 16 = 2*2*2*2....................there are four times 2 ....can't be grouped into 3

Answer 15

if you remember cube root of 2........you can find 16^(1/3)

Answer 16

or if you are free to use logarithmic tables

Answer 17

you know that there is a formula for 16^(1/3)

\[\huge\color{red}{a^{\frac{b}{c}}=\sqrt[c]{a^b}}\]
in your case,
a=16
b=1
c=3

Answer 18

So \[\huge\color{red}{16^{\frac{1}{3}}=\sqrt[3]{16}=\sqrt[3]{(2^3) \times 2}=2\sqrt[3]{2}}\]

Answer 19

w = 3+16^(1/3) would be exactly, \[\huge\color{red}{w=3+2\sqrt[3]{2}}\]

Answer 20

thank you everyone :)

Answer 21

Anytime, yw!