Which of the following are irrational numbers?
√48
32
−1
16
45
15
44
Which of the following are irrational numbers? √48 32 −1 16 45 15 44
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Which of the following are irrational numbers?
√48
32
−1
16
45
15
44
The irrational number from your list is √48.
Explanation:
Irrational numbers are numbers that cannot be expressed as a simple fraction, meaning they cannot be written as the ratio of two integers. The square root of 48 (√48) simplifies to 4√3, which is irrational because √3 is not a perfect square and cannot be expressed as a fraction.
The other numbers (32, −1, 16, 45, 15, 44) are all integers, which are rational numbers because they can be expressed as fractions (e.g., 32/1).
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The irrational numbers from the list are √48.
Explanation:
Irrational numbers cannot be expressed as a fraction of two integers. √48 can be simplified to 4√3, which is irrational (since √3 is not a perfect square and cannot be expressed as a fraction). The other numbers (32, -1, 16, 45, 15, 44) are all integers and thus rational, as they can be expressed as fractions (e.g., 32/1, -1/1, etc.).
If you have more questions or need further assistance, feel free to ask!
To identify which of the numbers are irrational, we need to recall that irrational numbers cannot be expressed as a fraction of two integers and their decimal representation is non-repeating and non-terminating.
1. √48: This can be simplified to (4sqrt{3}). Since (sqrt{3}) is irrational, (sqrt{48}) is also irrational.
2. 32: This is a whole number (integer) and can be expressed as (frac{32}{1}), so it is rational.
3. −1: This is also a whole number and can be expressed as (frac{-1}{1}), so it is rational.
4. 16: This is a whole number (integer) and can be expressed as (frac{16}{1}), so it is rational.
5. 45: This is a whole number (integer) and can be expressed as (frac{45}{1}), so it is rational.
6. 15: This is a whole number (integer) and can be expressed as (frac{15}{1}), so it is rational.
7. 44: This is a whole number (integer) and can be expressed as (frac{44}{1}), so it is rational.
From the above analysis, the only irrational number in the list is:
– √48
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