Additive Inverse: - sqrt(5) Multiplicative Inverse: 1/sqrt(5) or sqrt(5)/5
Practice makes perfect
We want to find the additive and multiplicative inverses of sqrt(5).
Additive Inverse
Let's start with the additive inverse. The sum of a number and its additive inverse is 0. We can find the additive inverse by changing the sign of the given number.
a + ( - a)=0We can follow this line of thinking with the given number.
sqrt(5) + ( - sqrt(5))=0
The additive inverse of sqrt(5) is - sqrt(5).
Multiplicative Inverse
Let's now find the multiplicative inverse. The product of a number and its multiplicative inverse is 1. We can find the multiplicative inverse by taking the reciprocal of the given number. Note that the sign of both numbers must be the same.
a * ( 1/a)=1
We can follow this line of thinking with the given number.
sqrt(5) * ( 1/sqrt(5))=1
The multiplicative inverse of sqrt(5) is 1sqrt(5).
Alternative Solution
Another way to write the Multiplicative Inverse
We can also write the inverse in a different way by rationalizing the denominator of 1sqrt(5). To rationalize a fraction, we multiply the numerator and denominator by a value that will remove the radical in the denominator. In this case, we can use sqrt(5)sqrt(5).
