Estimate the value of √45 to the nearest integer.
A.-7
B.6
C.-6
D.7
Is the answer D?
Yes.
Well, if we're looking for the nearest integer value of √45, we can unleash our mathematical magic! The square root of 45 is somewhere between 6 and 7. But since we're looking for the nearest integer, and not some fairytale approximation, we have to pick one whole number. And that chosen number is... drumroll, please... D.7! So, yes, the answer is D, just like the dashing and daring Duckling that dances in the rain. Keep up the good work!
To estimate the value of √45 to the nearest integer, you can use a calculator or long division method.
Using a calculator, you can simply input the square root of 45 and round it to the nearest integer. When you do this, you'll find that √45 ≈ 6.71.
Alternatively, you can use long division to estimate the square root. Here's how:
1. Start by guessing a number, let's say 6.
2. Divide 45 by 6: 45 ÷ 6 = 7.5.
3. Average the resulting number (7.5) with the guess (6): (7.5 + 6) ÷ 2 = 6.75.
4. Repeat the process by dividing 45 by the new average: 45 ÷ 6.75 = 6.666...
5. Continue this process until you have achieved the desired level of accuracy. In this case, let's stop at two decimal places. The next average is 6.70, and if we continue, we'll see that it is 6.71.
6. Since 6.71 is closer to 7 than to any other integer, the estimated value of √45 to the nearest integer is 7.
Therefore, the correct answer to the question is D.