1) any of the rational numbers as well as their negative opposites
2) the square root of any number
3) a number that cannot be obtained by the division of two integers
4) a number that includes a repeating decimal
5 answers
The correct definition of an irrational number is:
Irrational numbers cannot be expressed as a fraction of two integers and do not have a repeating or terminating decimal representation. Examples include numbers like π (pi) and √2.
To estimate the value of \( 6 \times 2 - \sqrt{6} \), we can break it down step-by-step:
Calculate \( 6 \times 2 \): \[ 6 \times 2 = 12 \]
Estimate \( \sqrt{6} \): \(\sqrt{6}\) is approximately \( 2.45\) (since \(2.4^2 = 5.76\) and \(2.5^2 = 6.25\), we can estimate it's between those two).
Subtract the estimated square root from \(12\): \[ 12 - 2.45 \approx 9.55 \]
Now let's compare that with the given choices:
The best estimate from the choices provided would be 9.8, as it is the closest to our calculated result of approximately \(9.55\).
To determine which statement is true about the square root of 28, we'll evaluate its value:
Since \(25 < 28 < 36\), we can conclude that: \[ 5 < \sqrt{28} < 6 \]
Now, let's analyze how close \( \sqrt{28} \) is to these integers:
\[ \sqrt{28} \approx 5.29 \]
Thus, it is indeed between \(5\) and \(6\), and since \(5.29\) is closer to \(5\) than to \(6\), the true statement about the square root of 28 is:
It is between 5 and 6, probably closer to 5.
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