which of the following are irrational numbers

Question

pi
62
square root of 47
square root of 26

Answer 1

Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They have non-repeating, non-terminating decimal expansions.

Let's analyze each of the given numbers:

1. π (pi): This is an irrational number.
2. 62: This is a whole number (integer) and can be expressed as a fraction (62/1), so it is not irrational.
3. √47: This is an irrational number because 47 is not a perfect square.
4. √26: This is also an irrational number because 26 is not a perfect square.

In conclusion, the irrational numbers from your list are:

• π
• √47
• √26

Answer 2

square root of 48
3 and 2/22
0
-7

Answer 3

Let's evaluate each of the given numbers to determine which are irrational:

1. √48: This can be simplified as √(16 * 3) = 4√3. Since √3 is an irrational number, √48 is also irrational.

2. 3 and 2/22: This can be expressed as $3+\frac{2}{22}=3+\frac{1}{11}=\frac{34}{11}$, which is a rational number because it can be expressed as a fraction of two integers.

3. 0: This is a rational number since it can be expressed as 0/1.

4. -7: This is also a rational number because it can be expressed as a fraction (-7/1).

In conclusion, from your list, the only irrational number is:

• √48

All the other numbers (3 and 2/22, 0, -7) are rational.

Answer 4

square root of 9
-716
300.666...

Answer 5

Let's analyze each of the given numbers:

1. √9: This equals 3, which is a rational number because it can be expressed as a fraction (3/1).

2. -716: This is a whole number (integer) and can be expressed as a fraction (-716/1), so it is a rational number.

3. 300.666...: The decimal representation 300.666... can also be written as $300+\frac{2}{3}$ (since 0.666... is equal to $\frac{2}{3}$). This can be expressed as a fraction, making it a rational number.

In conclusion, none of the numbers listed are irrational. All are rational:

• √9 = 3 (rational)
• -716 (rational)
• 300.666... (rational)

Answer 6

94
square root of 194
pi
341

Answer 7

Let's evaluate each of the given numbers to determine which are rational or irrational:

1. 94: This is a whole number (integer) and can be expressed as a fraction (94/1), so it is a rational number.

2. √194: The square root of 194 is not a perfect square—it cannot be expressed as a fraction of two integers. Therefore, √194 is an irrational number.

3. π (pi): This number is well-known to be an irrational number as it cannot be expressed as a fraction of two integers and has a non-terminating, non-repeating decimal expansion.

4. 341: This is also a whole number (integer) and can be expressed as a fraction (341/1), so it is a rational number.

In conclusion, the irrational numbers from your list are:

• √194
• π

The rational numbers are:

• 94
• 341