show an example of an irrational number between 9 and 11.

Question

1. square root of 20
2. square root of 99
3. square root of 100
4. square root of 10

Answer 1

To find an irrational number between 9 and 11 from the options given, we can analyze each option:

1. Square root of 20:
   \(\sqrt{20} \approx 4.47\) (not between 9 and 11)

2. Square root of 99:
   \(\sqrt{99} \approx 9.95\) (this is between 9 and 11 and is irrational)

3. Square root of 100:
   \(\sqrt{100} = 10\) (this is rational)

4. Square root of 10:
   \(\sqrt{10} \approx 3.16\) (not between 9 and 11)

The only option that is an irrational number between 9 and 11 is square root of 99.

Answer 2

what is the least integer whose square root is an irrational number between 5 and 7?
1. 6
2. 13
3. 26
4. 25

Answer 3

To find the least integer whose square root is an irrational number between 5 and 7, we first identify the range of values for \(x\) where \(5 < \sqrt{x} < 7\) can be squared:

1. Squaring the lower bound:
   \[5^2 = 25\]

2. Squaring the upper bound:
   \[7^2 = 49\]

So, we need \(25 < x < 49\) for \(\sqrt{x}\) to be irrational and between 5 and 7.

Now we can evaluate the options provided:

1. 6:
   \(\sqrt{6} \approx 2.45\) (not between 5 and 7)

2. 13:
   \(\sqrt{13} \approx 3.61\) (not between 5 and 7)

3. 26:
   \(\sqrt{26} \approx 5.1\) (this is between 5 and 7 and is irrational)

4. 25:
   \(\sqrt{25} = 5\) (this is rational)

The least integer from the options provided that has an irrational square root between 5 and 7 is 26.

Answer 4

show an example of a rational number that is between the square root of 10 and the square root of 11.
1. 10/3
2. 16/5
3. 3.1
4. 3.4

Answer 5

To determine a rational number that is between \(\sqrt{10}\) and \(\sqrt{11}\), we first calculate the approximate values of these square roots:

• \(\sqrt{10} \approx 3.162\)
• \(\sqrt{11} \approx 3.317\)

Now, we need to find a rational number between 3.162 and 3.317 from the provided options:

1. 10/3:
   \(\frac{10}{3} \approx 3.333\) (this is greater than \(\sqrt{11}\))

2. 16/5:
   \(\frac{16}{5} = 3.2\) (this is between \(\sqrt{10}\) and \(\sqrt{11}\))

3. 3.1:
   (this is less than \(\sqrt{10}\))

4. 3.4:
   (this is greater than \(\sqrt{11}\))

The rational number from the options provided that is between \(\sqrt{10}\) and \(\sqrt{11}\) is 16/5.

Answer 6

which irrational number is between the square root of 14 and the square root of 18?
1. the square root of 19
2. the square root of 15
3. the square root of 13
4. the square root of 10

Answer 7

To determine which irrational number is between \(\sqrt{14}\) and \(\sqrt{18}\), we first need to find the approximate values of these square roots:

• \(\sqrt{14} \approx 3.742\)
• \(\sqrt{18} \approx 4.243\)

Now we want to find an irrational number from the given options that lies between approximately 3.742 and 4.243.

1. Square root of 19:
   \(\sqrt{19} \approx 4.359\) (this is greater than \(\sqrt{18}\))

2. Square root of 15:
   \(\sqrt{15} \approx 3.873\) (this is between \(\sqrt{14}\) and \(\sqrt{18}\))

3. Square root of 13:
   \(\sqrt{13} \approx 3.606\) (this is less than \(\sqrt{14}\))

4. Square root of 10:
   \(\sqrt{10} \approx 3.162\) (this is also less than \(\sqrt{14}\))

The irrational number from the options provided that lies between \(\sqrt{14}\) and \(\sqrt{18}\) is the square root of 15.

Answer 8

how many irrational numbers are there between the square root of 11 and the square root of 17?
1. 4 numbers
2. 28 numbers
3. 6 numbers
4. an infinite number

Answer 9

Between any two distinct real numbers (including irrational numbers), there are infinitely many irrational numbers. Thus, the number of irrational numbers between \(\sqrt{11}\) and \(\sqrt{17}\) is:

An infinite number.

So, the correct answer is 4. an infinite number.