Video Transcript
Calculate 12 times the square root
of three multiplied by seven times the square root of three.
In this question, we are asked to
evaluate an expression involving the product of real numbers. If we begin by looking at the
expression that we are asked to evaluate, we can note that there are two factors of
root three and two integer factors.
When applying operations on real
numbers, we usually want them to be in the same form so that we can evaluate the
operation. In this case, we can recall that
the multiplication of real numbers is associative and commutative. So we can evaluate the product in
any order and reorder the product to multiply the integer parts and radical parts
separately.
We get 12 times seven multiplied by
root three times root three. We can first calculate that 12
times seven is equal to 84. We can then recall that for any
nonnegative real number 𝑎, the square root of 𝑎 times the square root of 𝑎 is
equal to 𝑎. We can apply this result with 𝑎
equal to three to see that root three times root three is equal to three. Therefore, our expression
simplifies to give 84 times three. We can then calculate that 84 times
three is equal to 252.
Hence, we were able to show that 12
root three times seven root three is equal to 252.
