Question

Solve the equation x² = 36 for x A. -36, 36 B. -18, 18 C. -6, 6 D. -3, 3

Answer 1

`x = √(36) =` ± 6

Explanation:

This one's easy if you just think about it for a moment:

"What number squared equals 36?"

Even if they don't give you choices, couldn't you figure that out?

2 squared is 4; 3 squared is 9; 4 squared is 16; 5 squared is 25; and 6 squared is 36.

If you haven't memorized those yet, it would benefit you to start working on them. Knowing your squares up to 10 will save you a lot of time in future problems. And up to 15 is pretty easy to remember too. Then think about the numbers like 20, 30, 40, etc, and 100, 200, etc. Don't memorize all those, but get comfortable with their forms. For example: 40 squared is just the 4 squared, which is 16, plus two zeroes: one from each of the 40's. So it's 1600

Anyway, that just gives you the answer, and from there of course you'd pick C, but it doesn't "solve the equation." But that's easy too:

x² = 36

We'd like for x to be "by itself" wouldn't we? With nothing acting on it. How can we cancel out a square term? By taking the square root, right? So take the square root of both sides:

`\sqrt{x^(2) } = √(36)`

Look familiar? The square root cancels out or "undoes" the square, so:

`x = √(36)`

And because you memorized all the squares up to 10, you quickly know that the square root of 36 is 6, without having to reach for your calculator. So let's show that step:

`x = √(36) = 6`

And we usually don't bother with the negative root, but it's true that squaring -6 (negative six) does also give us +36 (positive 36), so let's include that in our answer:

`x = √(36) =` ±6