Find The Square Root Of 85 To The Nearest Tenth
Alright, math adventurers! Gather 'round, because we're about to embark on a quest for a number that's been a bit of a mystery – the square root of 85! Now, you might be thinking, "Square root? That sounds like something out of a wizard's spellbook!" And you know what? You're not entirely wrong. It feels a little bit like magic, but we're going to demystify it, and I promise, it's going to be a blast.
Imagine you're trying to build the perfect square. Not just any square, mind you. We're talking about a square so symmetrical, so flawless, that it would make a geometry teacher weep with joy. If the area of this magnificent square is 85, then the length of each of its sides is our elusive square root of 85. So, we're essentially asking: "What number, when multiplied by itself, gets us as close as humanly possible to 85?"
Now, finding that exact number can be a tad tricky. It's not like finding the square root of, say, 81. We all know that 9 times 9 is 81. Easy peasy, lemon squeezy! Or how about 100? Well, that's a no-brainer; 10 times 10 equals 100. Our number, 85, falls neatly in between these perfect squares. It's like a mischievous little imp, hiding just out of our easy-counting reach. But fear not! We're going to wrangle this imp into submission, and we're going to aim for the nearest tenth, like a seasoned sharpshooter.
Think of it like trying to guess the exact weight of a really plump, delicious watermelon. You can't just say "heavy." You need a bit more precision, right? Maybe you'll say "around 15 pounds." But what if you could get even closer? "About 15.2 pounds." That's the kind of precision we're aiming for with our square root of 85. We want to get to that first decimal place, that tenth of a pound, that glorious .1.
So, let's get our metaphorical detective hats on. We know 9 squared is 81. That's pretty darn close to 85, wouldn't you agree? It’s like being at the front door of a party, almost there! But 85 is more than 81, so our square root has to be more than 9. Now let's try the next whole number up: 10. We know 10 squared is 100. That's a bit too far past 85, isn't it? It's like accidentally crashing the party and then trying to sneak out unnoticed. So, our answer is definitely between 9 and 10. We've narrowed it down!
Now comes the fun part – the "getting closer" part. We're going to start nudging our number from 9. We need to figure out what to add to 9 to get us to that magic 85. We're not going to just randomly pick numbers, oh no. We’re going to use a little bit of tried-and-true mathematical finesse. Imagine you’re trying to dial in a perfect radio station. You get close, you hear a bit of static, you fine-tune the dial just a hair. That's what we're doing!
Let's try a number just a little bit bigger than 9. How about 9.1? What's 9.1 multiplied by itself? Well, that's 9.1 x 9.1. If you were to do the multiplication, you'd get 82.81. Still a bit too small, right? We're getting warmer, but not quite there. Think of it like holding a perfectly warm mug of cocoa – it's nice, but maybe you want it just a tiny bit hotter.
So, we need to go a little higher. What about 9.2? Let's multiply 9.2 by itself: 9.2 x 9.2. That gives us 84.64. Ooh, we are SO close now! We can practically taste the perfectly square cake! 84.64 is nipping at the heels of 85. It's like being at the finish line, with only a few inches to go.
What about 9.3? Let's see what 9.3 squared is: 9.3 x 9.3. That equals 86.49. Whoa there! We've zoomed past 85! That's like running through the finish line and doing a celebratory cartwheel on the other side. So, our number is definitely less than 9.3.
So, where does that leave us? We have 9.2 squared giving us 84.64, which is very close to 85. And we have 9.3 squared giving us 84.69, which is a little over 85. We need to decide which one is nearest. We compare how far away each of those numbers is from 85.
How far is 84.64 from 85? It's 85 - 84.64 = 0.36 away.
How far is 86.49 from 85? It's 86.49 - 85 = 1.49 away.
See that? 84.64 is much, much closer to 85 than 86.49 is! It's like comparing a whisper to a shout – the whisper is much closer to what you’re trying to hear. So, 9.2 is our champion!
We've done it! The square root of 85, to the nearest tenth, is a magnificent 9.2!
Isn't that fantastic? We took a number that seemed a little shy, a little mysterious, and we brought it right into the light, to a neat and tidy decimal place. You've just conquered a bit of mathematical wilderness, and you should feel incredibly proud. So go forth, my friends, and remember: even the trickiest numbers can be tamed with a little curiosity and a sprinkle of enthusiasm. High fives all around!