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86 must lie between the whole numbers 9 and 10 beacuse 9 to the power of 2 = 81 and 1o to the pwoer of 2 = 100, and 86 lies between these values.

To one decimal place, 86 must lie between ___ and __

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To find the whole numbers between which 86 lies based on its square root, we can look at the squares of numbers around its square root.

  1. Calculate \( \sqrt{86} \):
    • \( 9^2 = 81 \)
    • \( 10^2 = 100 \)

Since \( 86 \) is between \( 81 \) and \( 100 \), we can conclude: \[ 9 < \sqrt{86} < 10 \]

Now, let's narrow it down to one decimal place.

Calculating the square root of 86 gives us approximately: \[ \sqrt{86} \approx 9.273 \]

Thus, to one decimal place, the square root of 86 lies between: \[ 9.2 \text{ and } 9.3 \]

Therefore, to one decimal place, 86 must lie between 9.2 and 9.3.

86 must lie between the whole numbers 9 and 10 because 9 to the power of 2 = 81 and 1o to the power of 2 = 100, and 86 lies between these values.
To one decimal place, 86 must lie between 9.2 and 9.3 because 9.2 to the power of 2 = 84.64 and 9.3 to the power of 2 = 86.49
To two decimal places, 86 lies between ___ and ___

To find the range in which 86 lies based on its square root, we want to narrow it down to two decimal places. We already know:

  • \( 9^2 = 81 \)
  • \( 10^2 = 100 \)
  • \( 9.2^2 = 84.64 \)
  • \( 9.3^2 = 86.49 \)

Now, we need to refine our search and find the decimal values that provide a better boundary around \( \sqrt{86} \).

First, let's calculate the squares of numbers between 9.2 and 9.3:

  1. Calculate \( 9.25^2 \): \[ 9.25^2 = 85.5625 \]

  2. Calculate \( 9.26^2 \): \[ 9.26^2 = 85.8276 \]

  3. Calculate \( 9.27^2 \): \[ 9.27^2 = 86.1129 \]

Now we have:

  • \( 9.25^2 = 85.5625 \) (less than 86)
  • \( 9.26^2 = 85.8276 \) (less than 86)
  • \( 9.27^2 = 86.1129 \) (greater than 86)
  • \( 9.3^2 = 86.49 \) (greater than 86)

So, we can find that \( \sqrt{86} \) lies between \( 9.27 \) and \( 9.28 \).

To two decimal places, we can summarize that:

86 lies between 9.27 and 9.28.

would 86 eventually stop or go on forever, because 86 is a ?? number

The number 86 is a whole number (or an integer), which means it is a non-decimal number and can be expressed without fractions or decimal points. Whole numbers include all positive integers (0, 1, 2, 3, ...) and, in this case, 86 is one of those integers.

As a specific whole number, 86 does not "go on forever." Whole numbers are distinct values, and 86 itself is finite.

However, when you're discussing the sequence of whole numbers, you could say that whole numbers go on indefinitely as you can always find the next whole number by adding one more to any given whole number. So while 86 itself is just a single, fixed value, the whole numbers as a category do continue indefinitely in the positive direction.

In summary, 86 is a whole number, and whole numbers as a set continue infinitely, but 86 itself is a specific, finite value.

is 86 a rational number or irrational number?

The number 86 is a rational number.

Rational numbers are defined as any numbers that can be expressed as the quotient or fraction \(\frac{p}{q}\), where \(p\) is an integer and \(q\) is a non-zero integer. Since 86 can be written as \(\frac{86}{1}\), it fits this definition.

In contrast, irrational numbers cannot be expressed as fractions or ratios of integers; they have non-repeating, non-terminating decimal expansions (like \(\sqrt{2}\) or \(\pi\)).

So, to summarize: 86 is a rational number.