Tip:
Highlight text to annotate it
X
(male narrator) In this video,
we will look at solving equations
that have radicals in them-- specifically, odd roots.
The opposite of taking a root is to do an exponent.
In other words, if we have the cube root of x equals 4,
we need to do the opposite of a cube root
to remove the radical.
The opposite of a cube root
would be a 3rd power on both sides:
4 to the 3rd is 64, so x-- our variable--would be 64.
Let's take a look at some more involved problems
that require us to get rid of an odd root
by using an exponent.
In this problem, we have a cube root of 2x minus 5.
To get rid of that radical,
so we can access the inside part,
we do the exponent.
The opposite of cube root is 3rd power.
Doing the same thing on both sides,
cube root and 3rd power will be inverses,
leaving just 2x minus 5, equals 6 cubed, or 216.
We can quickly solve this remaining equation
by adding 5 to both sides; giving us 2x equals 221;
and finally, dividing by 2.
x is equal to 221, over 2,
or you can make that into a decimal...
by dividing 221 by 2 to get 110.5.
Let's try another example where we get rid of an odd root
by using an odd exponent.
In this problem, we have a 5th root.
We can get rid of a 5th root with a 5th power on both sides.
Fifth power and fifth roots are inverses,
leaving just the 4x minus 7,
equals 2 to the 5th, which is 32.
We can then solve by adding 7 to both sides,
and 4x is equal to 39.
Finally, dividing by 4 tells us that x is equal to 39 over 4.
By remembering that the opposite of a root is an exponent,
we can quickly solve problems with odd roots
by using exponents to clear the radical.