### Video Transcript

Find the additive inverse of eight
minus the square root of 135.

Remember, the additive inverse of a
number 𝑎 is the number that when added to 𝑎 gives zero. So, we need to find a number that
when we add it to eight minus the square root of 135, we get zero. And one way to answer this is to
use algebra. Let’s let 𝑥 be the additive
inverse of eight minus the square root of 135. Then, we know that the sum of 𝑥
and eight minus the square root of 135 is zero. And since we’re simply adding here,
we don’t actually need these parentheses or brackets.

We want to find the value of
𝑥. Remember, we’re trying to find the
additive inverse of our number. And so, we’re going to solve this
equation. We have 𝑥 plus eight minus the
square root of 135. So, we begin by subtracting eight
from both sides of our equation. On the left-hand side, that leaves
us with 𝑥 minus the square root of 135. And on the right-hand side, we get
negative eight. So, 𝑥 minus the square root of 135
is equal to negative eight. The opposite of subtracting is
adding. So, next, we add the square root of
135 to both sides. And so, we see that 𝑥 is equal to
negative eight plus the square root of 135. And it’s quite usual to write the
positive number first.

And so, we can say that the
additive inverse of eight minus the square root of 135 is the square root of 135
minus eight. Now, it follows that since we know
that the additive inverse of a number and that number sum to zero. We can check our solution by adding
eight minus the square root of 135 and the square root of 135 minus eight. So, that’s eight minus the square
root of 135 plus the square root of 135 minus eight. So, we see that eight minus eight
is zero and negative root 135 plus root 135 is zero. So, we get zero as required.