Question Video: Solving One-Term Quadratic Equations Mathematics

Solve 𝑥²= 200, leaving your answer in surd format in its simplest form.

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Video Transcript

Solve 𝑥 squared equals two hundred, leaving your answer in surd format in its simplest form. So it says surd format here. That might say in radical format or it might say expressing it as a multiple of irrational number; you could encounter that in either of those forms. So let’s just write that expression out: 𝑥 squared equals two hundred. Well if we’re solving that, we want to know what 𝑥 equals. So what we have to do to 𝑥 squared to turn it into 𝑥? Well, we’ve got to take the square root of both sides of the equation. So the square root of 𝑥 squared is 𝑥 and that’s equal to the square root of two hundred. But it’s not quite as simple as that because it could be positive root two hundred or it could be negative root two hundred because negatives times negatives make positives.

So there we are, 𝑥 is equal to plus or minus root two hundred. Well we’ve solved it, and but we still need to put it into its simplest form. So we’ve got to try to look for factors of two hundred, which are square numbers and we want the biggest one of those that we can. So I’m looking for the largest square factor that I can find of two hundred and then times something else. So two hundred, so we’re gonna divide by two, divide by three, divide by four until we find the other factor which is a square number. So two hundred divided by two is a hundred. Ah, that is a square number. So it’s a hundred times two. And we can split the hundred and the two out remember, so that’s plus or minus the square root of a hundred times the square root of two. And because the square root of a hundred is ten. That becomes ten times root two or ten root two. So our final answer here is plus or minus ten root two.

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