Video: Finding the Solution Set of Radical Equations

Find the value of 𝑥 for which √1225 = √400 + √𝑥.

02:40

Video Transcript

Find the value of 𝑥 for which root 1225 is equal to root 400 plus root 𝑥.

Okay, to solve this problem, obviously we need to find the root of 1225 and square root of 400 to enable us to then figure out what 𝑥 would be. Using a calculator, we’ve just found the values of the square root of 1225 cause that would be 35, and we’d also know that the square root of 400 would be 20. I’m also gonna show you quickly how you’d do it if it was a non-calculator paper.

If it was on a non-calculator paper, the part that might actually cause you a bit of trouble would be the square root of 1225 cause you may know it’s 35, that’s great if you do. But if you don’t, I’m just gonna show you how you can actually find it another way. To do it, we’d actually use this rule which says that root 𝑎 multiplied by root 𝑏 is equal to root 𝑎𝑏. Now, to consider what the two values would be, we can actually look at 1250. Well, 1250 is equal to five multiplied by 250, but neither of those here would give us any square numbers. So let’s remember the one we’re trying to simplify, as said we wanted, is a square number.

Okay, so then we can look at 50 multiplied by 25. We see actually yeah, 1250 would be made by 50 multiplied by 25. Great so long as you got a 25, that’s one of our square numbers. Now you think, right, well that’s 1250. If we wanted 1225, well that’s actually 25 less. So that’s gonna be equal to 25 multiplied by 49 cause I said one less than 50. Great. So now, here we actually have two square numbers. So we can now work out the value of the square root of 1225 cause root 25 is five, square root of 49 is seven. So then we multiply five and seven, and we get 35. I mean, looks that that’s just one way of looking at how you solve this problem without a calculator. And it’s got a bit of trial and error, a bit of actually problem solving there.

But now we may head back to the question. There, we’ve got the values of the square roots of 1225 and 400 to solve. Okay. So first thing we do is subtract 20 from each side which gives us 15 is equal to root 𝑥. And next, we are to square each side. And then once we’ve done that, we’re gonna find the value of 15 squared.

So there we have it; our final answer: 𝑥 is equal to 225.

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