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Have you ever encountered a square root that left you scratching your head? You know, the ones that aren't nice, neat whole numbers? We're talking about numbers like the square root of 45. It's not a perfect square like 9 (3 x 3) or 25 (5 x 5), so how do we figure it out? Don't worry, approximating square roots is easier than you think!
Let's break down how to approximate the square root of 45 to the hundredths place, and the best part is, we can do it without even glancing at a calculator!
Think of Perfect Squares as Your Guideposts
Imagine perfect squares as friendly landmarks on a number line. You know that 36 (6 x 6) is a perfect square, and so is 49 (7 x 7). Since 45 sits comfortably between these two numbers, we know its square root must fall somewhere between 6 and 7.
Narrowing it Down
Now, let's get a little closer. 45 is only 4 away from 49 and 9 away from 36. This tells us that the square root of 45 will be a bit closer to 7 than it is to 6.
"Think of it like a treasure hunt! You're using the clues of perfect squares to zero in on your target."
Taking a Calculated Guess
Since 45 is closer to 49, let's start by trying a decimal value a bit closer to 7. How about 6.7? To see if we're on the right track, let's square 6.7 (multiply it by itself).
6.7 x 6.7 = 44.89
That's pretty close to 45, but we can get even closer!
Fine-Tuning Our Approximation
Let's bump our guess up just a tad to 6.71 and see what happens when we square it.
6.71 x 6.71 = 45.0241
Wow! We're now just a hair above 45. This means that 6.71 is a very accurate approximation of the square root of 45 to the hundredths place.
The Power of Approximation
Approximating square roots is a valuable skill, even in our calculator-driven world. It helps you understand the relationships between numbers and strengthens your number sense. So next time you encounter a tricky square root, remember these steps and unlock the answer with confidence!
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