Welcome to How to Simplify a Cube Root (Non-Perfect Cubes) with Mr. J! Need help with simplifying cube roots? You're in the right place!
Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with how to simplify cube roots of non-perfect cubes. Mr. J will go through examples of simplifying cube roots and explain the steps of how to simplify cube roots of non-perfect cubes.
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welcome to math with Mr Jay
[Music]
in this video I'm going to cover how to
simplify cube roots let's jump into
number one where we have the cube root
of 48. now 48 is not a perfect Cube so
we're not going to get a nice clean cut
whole number for our answer but we can
simplify this cube root we can break it
down so to speak we're going to do this
by looking for factors of 48 that are
perfect cubes and then find their cube
root we will then pull that cube root
out now to the right I have the first 10
perfect cubes knowing and being familiar
with these or as many of these as you
can will make simplifying cube roots and
working with cube roots in general much
easier so are any of the first 10
perfect cubes a factor of 48 yes 8 is a
factor of 48. we know that 8 times six
equals 48 8 and 6 are factors of 48.
they go into 48 so to speak so let's
rewrite the cube root of 48 as the cube
root of 8 times 6. now the
multiplication or product property of
cube root lets us split this into the
cube root of eight times the cube root
of 6 meaning
we have
the cube root of eight
times
the cube root
of 6. this is still equivalent to the
cube root of 48. we're not changing the
value of anything at all now we can take
the cube root of eight which is two two
times two times two equals eight so
again the cube root of eight is two so
we end up with two
times
the cube root of six and that's our
final simplified answer we can't
simplify or break this down any further
so again our final simplified answer
2 times the cube root of 6. let's move
on to number two where we have the cube
root of 250. 250 is not a perfect Cube
but we can simplify we need to look for
factors of 250 that are perfect cubes
well 125 times 2 equals 250 and 125 is a
perfect Cube since there's a factor of
250 that's a perfect Cube we can
simplify we can rewrite this as the cube
root of 125
times
2. now let's split this into the cube
root
of 125
times
the cube root
of 2. now we can take the cube root of
125 which is 5 5 times 5 times 5 equals
125. again the cube root of 125 is 5. so
this is going to equal five
times the cube root
of 2 and that's our final simplified
answer
5 times the cube root of 2. we cannot
simplify or break that down any further
so there you have it there's how to
simplify cube roots I hope that helped
thanks so much for watching
until next time peace
okay
