To one decimal place, 26 must lie between 5.1 and 5.2 because \(5.1^2 = 26.01\) and \(5.2^2 = 27.04\). Therefore, 26 lies between these squared values.
26 must lie between the whole numbers 5 and 6 because 5 to the power of 2 = 25 and 6 to the power of 2 = 36, and 26 lies between these values.
to one decimal place, 26 must lie between __ and __ because
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I apologize for the oversight. Let's determine the correct whole-number approximations for \( \sqrt{26} \).
To one decimal place, 26 must lie between 5.0 and 5.1 because:
- \(5.0^2 = 25.0\)
- \(5.1^2 = 26.01\)
Since \(26\) is greater than \(25\) and less than \(26.01\), it confirms the approximation. Thank you for your patience!
to one decimal place, 26 must lie between 5.0 and 5.1 because 5 to the power of 2 = 25 and 5.1 to the power of 2 = 26.01, and 26 lives between the values.
To Two decimal places, 26 must lie between ___ and __
To two decimal places, 26 must lie between 5.09 and 5.10 because:
- \(5.09^2 = 25.9081\)
- \(5.10^2 = 26.01\)
Since \(26\) is greater than \(25.9081\) and less than \(26.01\), this confirms that \( \sqrt{26} \) lies between these two values.
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eventually stop or go on forever
If we were to continue this process, it would eventually stop because \(26\) is a rational number.
Rational numbers can be expressed as the quotient of two integers, and their decimal representations either terminate or repeat. Since \(26\) is a perfect square of \(5.099\), which can be approximated with a finite number of decimal places, the process of narrowing down the interval will eventually lead to an exact representation.
I apologize for any confusion, but actually, 26 is not an irrational number; it is a rational number.
Rational numbers are those that can be expressed as a fraction of two integers. The number 26 can be expressed as \( \frac{26}{1} \), confirming that it is rational.
However, if we consider \( \sqrt{26} \), that value is indeed an irrational number. The process of narrowing down the interval around \( \sqrt{26} \) would indeed go on forever, as the decimal expression for \( \sqrt{26} \) does not terminate or repeat.
To clarify:
- 26 is rational.
- \( \sqrt{26} \) is irrational, and thus the decimal approximation process would go on forever.
So, if the question is about \( \sqrt{26} \), then yes, it would go on forever. Thank you for your understanding.