Home > Algebra > Simplification of Radical Expressions

How do you simplify #root3(216,000)#?

Answer 1

Hazel Anglin

#root(3)(216,000) =60#

Extracting the most obvious cube: #color(white)("XXX")216,000 = 216 xx 10^3#

Then factor out basic primes until we get to a complete factoring: #color(white)("XXX")=2xx108xx10^3#

#color(white)("XXX")=2^2xx54xx10^3#

#color(white)("XXX")=2^3xx27xx10^3#

#color(white)("XXX")=2^3xx3xx9xx10^3#

#color(white)("XXX")=2^3xx3^3xx10^3# #color(white)("XXXXXX")#In practice we probably would have recognized the cube factors before going this far.

Therefore #color(white)("XXX")root(3)(216,000) = root(3)(2^3xx3^3xx10^3) = 2xx3xx10 =60#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.