Question Video: Finding the Additive Inverse of a Given Real Number Involving Square Roots Mathematics

Find the additive inverse of 8 − √135.

02:13

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.

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