The diagonal of a square equals √2 times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?
The diagonal of a square is the hypotenuse of a right triangle with the sides being the two sides of the square. According to Pythagorean theorem, the length of the diagonal is the square root of the sum of the squares of the two sides.
Let's denote "s" as the length of each side of the square park. We are given that the length of each side is 700 feet. Therefore, s = 700.
According to the information given, the length of the diagonal (d) is √2 times the side length.
Therefore, d = √2 * s.
We are given that √2 is approximately 1.4. So we can substitute this value into the formula:
d = 1.4 * s
Substituting the value of s = 700:
d = 1.4 * 700
d = 980
Therefore, the approximate length from one corner to an opposite corner of the square park is 980 feet.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?
√40 is between ___ and ___
To find the whole number and the rational number to the nearest half that √40 is between, we can use a number line.
First, let's determine the whole number that √40 is closest to. The square root of 40 is approximately 6.32. The whole number closest to 6.32 is 6.
Next, we need to find the rational number to the nearest half that √40 is between. To do this, we can compare the value of √40 to the square of both 6 and 7.
The square of 6 (6^2) is 36, which is less than 40. The square of 7 (7^2) is 49, which is greater than 40.
This tells us that √40 is between 6 and 7.
Now, let's find the rational number to the nearest half between 6 and 7. The halfway point between 6 and 7 is 6.5.
Therefore, √40 is between 6 and 6.5 on the number line.
are you sure?
I apologize for the mistake. Let's correct it:
To find the whole number and the rational number to the nearest half that √40 is between, we can use a number line.
First, let's determine the whole number that √40 is closest to. The square root of 40 is approximately 6.32. The whole number closest to 6.32 is 6.
Next, we need to find the rational number to the nearest half that √40 is between. To do this, we can compare the value of √40 to the square of both 6 and 7.
The square of 6 (6^2) is 36, which is less than 40. The square of 7 (7^2) is 49, which is greater than 40.
This tells us that √40 is between 6 and 7.
Now, let's find the rational number to the nearest half between 6 and 7. The halfway point between 6 and 7 is 6.5.
Therefore, √40 is between 6 and 6.5 on the number line.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?
between 8 and 8.5
between 8 and 8.5
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
between 7 and 7.5
between 8.5 and 9
To find the whole number and the rational number to the nearest half that √58 is between, we can use a number line.
The square root of 58 is approximately 7.62.
Now, let's find the whole number that √58 is closest to. The closest whole number to 7.62 is 8.
Next, let's find the rational number to the nearest half that √58 is between. To do this, we can compare the value of √58 to the square of both 8 and 8.5.
The square of 8 (8^2) is 64, which is greater than 58. The square of 8.5 (8.5^2) is 72.25, which is greater than 58.
This tells us that √58 is between 8 and 8.5.
Therefore, √58 is between 8 and 8.5 on the number line.
are you sure?
I apologize for the mistake.
To find the whole number and the rational number to the nearest half that √58 is between, we can use a number line.
The square root of 58 is approximately 7.63.
Now, let's find the whole number that √58 is closest to. The closest whole number to 7.63 is 8.
Next, let's find the rational number to the nearest half that √58 is between. To do this, we can compare the value of √58 to the square of both 8 and 8.5.
The square of 8 (8^2) is 64, which is greater than 58. The square of 8.5 (8.5^2) is 72.25, which is greater than 58.
This tells us that √58 is between 8 and 8.5.
Therefore, √58 is between 8 and 8.5 on the number line.