Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches. √3 2√3 √5 (a) Without using your calculator, approximate the decimal equivalent of each number to the
nearest tenth. (b) Order the ribbon sizes from least to greatest
√3:
3 is not a perfect square, but the nearest perfect squares are 1 and 4.
Thus √3 lies somewhere between √1 and √4.
Picture the numbers 1, 3 and 4 on a number line.
It takes 2 jumps to get from 1 to 3.
It takes 3 jumps to get from 1 to 4.
That means 3 is 2/3 of the way between 1 and 4.
So, we could estimate √3 to be 2/3 of the way between √1 and √4, or in other words, 2/3 of the way between 1 and 2.
1+ 2/3 = 1 2/3
To get this number to the nearest tenth, you would need to manually divide 2 by 3...or you might already know that 2/3 is 0.66666......
1 + 0.66666...... = 1.66666..... ~ 1.7 ( nearest tenth)
You can follow similar reasoning to find √5.
To approximate the decimal equivalent of each number to the nearest tenth without using a calculator, we can use some common approximations for square roots.
(a) Let's approximate the decimal equivalent of each number to the nearest tenth:
√3:
To approximate the decimal equivalent of √3, we can recall that √3 is slightly more than 1.7 and less than 1.8. Rounding it to the nearest tenth, we get 1.7.
2√3:
To approximate the decimal equivalent of 2√3, we can multiply the approximation we found for √3 by 2. So, 2√3 is approximately 2 * 1.7 = 3.4.
√5:
To approximate the decimal equivalent of √5, we can recall that √5 is slightly more than 2.2 and less than 2.3. Rounding it to the nearest tenth, we get 2.2.
So, the decimal approximations to the nearest tenth are:
√3 ≈ 1.7
2√3 ≈ 3.4
√5 ≈ 2.2
(b) Now, let's order the ribbon sizes from least to greatest:
1.7 is the smallest approximation among the given sizes.
Then we have 2.2.
And the largest approximation is 3.4.
So, the order of the ribbon sizes from least to greatest is:
√3 ≈ 1.7
√5 ≈ 2.2
2√3 ≈ 3.4
(a) To approximate the decimal equivalent of each number to the nearest tenth without using a calculator, we can use some estimation techniques.
√3 ≈ 1.7 (rounded to the nearest tenth)
To estimate the value of √3, we can compare it to the square root of 4, which is 2. Since 3 is closer to 4 than it is to 1, we can estimate that √3 is slightly less than 2.
2√3 ≈ 3.5 (rounded to the nearest tenth)
To estimate the value of 2√3, we can double the estimated value of √3. Doubling 1.7 gives us 3.4, which can be rounded to 3.5.
√5 ≈ 2.2 (rounded to the nearest tenth)
To estimate the value of √5, we can compare it to the square root of 4, which is 2. Since 5 is closer to 4 than it is to 9, we can estimate that √5 is slightly more than 2.
(b) Now let's order the ribbon sizes from least to greatest:
√3 < 2√3 < √5
Therefore, the ordered ribbon sizes from least to greatest are:
√3, 2√3, √5