Video Transcript
Find the value of the square root
of negative 55 multiplied by the cube root of negative 216.
In this question, we’re given an
expression that includes a cube root inside of a square root. We will begin with the inner
expression, that is, working out the value of the cube root of negative 216. We recall that the cube root of a
number 𝑛 is the number 𝑎 such that 𝑎 cubed is equal to 𝑛. And since negative 216 is negative,
we need to find a negative number that when cubed gives us negative 216. We know that 216 is a perfect cube,
since six cubed is equal to 216. Using the properties of perfect
cubes, this means that negative six cubed is equal to negative 216. And as such, the cube root of
negative 216 is negative six.
Substituting this into the
expression, we have the square root of negative 55 multiplied by negative six. Recalling that multiplying two
negative numbers gives a positive answer, and since 55 multiplied by six is 330,
then negative 55 multiplied by negative six is also 330. And our expression simplifies to
the square root of 330. We could try to evaluate this
further. However, on inspection, we note
that 330 is not a perfect square. And hence, the square root of
negative 55 multiplied by the cube root of negative 216 is the square root of
330.
