Video Transcript
Find the multiplicative inverse of
12 over the square root of 14.
In this question, we are asked to
find the multiplicative inverse of a given real number. We should start by recalling what
we mean by the multiplicative inverse. We can recall that the
multiplicative inverse of a number 𝑎 is the number 𝑏 whose product with 𝑎 gives
the multiplicative identity. So we need 𝑎 times 𝑏 to be equal
to one.
We can also recall that for any
nonzero real number 𝑎, we have that 𝑎 times one over 𝑎 is equal to one. So one over 𝑎 is the
multiplicative inverse of 𝑎. Hence, we can find the
multiplicative inverse of 12 over the square root of 14 by finding one divided by 12
over the square root of 14. We can recall that one divided by a
fraction is the same as its reciprocal. So one divided by 12 over root 14
is equal to root 14 over 12. We cannot simplify this any
further. So this is the multiplicative
inverse of 12 over root 14.
It is also worth noting that we can
check our answer by finding the product of 𝑎 and its multiplicative inverse, that
is, 12 over root 14 multiplied by root 14 over 12. We evaluate the product of
fractions by multiplying their numerators and denominators separately. So we obtain 12 root 14 over 12
root 14. We can cancel the shared factors in
the numerator and denominator to get one, confirming that the multiplicative inverse
of 12 over root 14 is the square root of 14 over 12.
