To which subset of real numbers does the following number belong?
10−−√
The number 10−−√ belongs to the subset of real numbers as it is a result of a square root operation.
To which subset of real numbers does the following number belong?
10−−√
1. rational numbers
2. irrational numbers
3. whole numbers, integers, rational numbers
To determine the subset of real numbers to which 10−−√ belongs, we need to consider whether it is a rational or irrational number.
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. An irrational number cannot be expressed as a fraction and its decimal representation goes on indefinitely without repeating.
In this case, since the square root of 10 is not a perfect square, 10−−√ is an irrational number. Therefore, the subset of real numbers to which it belongs is "2. irrational numbers."
To determine the subset of real numbers to which the number 10−−√ belongs, we need to evaluate its value.
10−−√ can be written as 10^(1/2) since the square root (√) is equivalent to raising a number to the power of 1/2.
Evaluating 10^(1/2), we find:
10^(1/2) = √10 ≈ 3.1622
Therefore, the number 10−−√ belongs to the subset of real numbers between 3 and 4 (inclusive), expressed as [3, 4].
To determine the subset of real numbers to which the number 10-√ belongs, we need to analyze its characteristics.
The expression 10-√ involves the square root (√) operation, which means we need to consider the behavior of the square root function.
The square root of a non-negative real number always produces a non-negative real number. This means that √x is only defined for x ≥ 0.
In our case, we have 10-√. Since 10 is a positive number, the expression √(10) is a valid square root, resulting in a non-negative real number.
Hence, the expression 10-√ will give us a non-negative real number.
Therefore, the number 10-√ belongs to the subset of non-negative real numbers, which can be denoted as [0, +∞). This subset includes all real numbers greater than or equal to zero.