Which of the following is an irrational number between 5 and 7: √6,√12 ,√27 , √36?
(1 point)
25 answers
The only number that is an irrational number between 5 and 7 is √6.
What is the largest integer whose square root is an irrational number between 3 and 4?(1 point)
The largest integer whose square root is an irrational number between 3 and 4 is 15.
Find a rational number between 2 and using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 7, we'll add the two numbers together and divide by 2.
Sum of the numbers: 2 + 7 = 9.
Dividing the sum by 2: 9 ÷ 2 = 4.5.
Since 4.5 is not a mixed number, we can convert it to a mixed number by separating the whole number part and the fractional part.
Whole number part: 4.
Fractional part: .5.
Converting the fractional part to a fraction: .5 = 1/2.
Therefore, the rational number between 2 and 7 is 4 1/2.
Sum of the numbers: 2 + 7 = 9.
Dividing the sum by 2: 9 ÷ 2 = 4.5.
Since 4.5 is not a mixed number, we can convert it to a mixed number by separating the whole number part and the fractional part.
Whole number part: 4.
Fractional part: .5.
Converting the fractional part to a fraction: .5 = 1/2.
Therefore, the rational number between 2 and 7 is 4 1/2.
Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 2 1/4, we'll add the two numbers together and divide by 2.
Converting 2 1/4 to an improper fraction: 2 1/4 = 9/4.
Sum of the numbers: 2 + 9/4 = 8/4 + 9/4 = 17/4.
Dividing the sum by 2: (17/4) ÷ 2 = 17/4 ÷ 2/1.
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction: 17/4 ÷ 2/1 = 17/4 * 1/2.
Multiplying the fractions: 17/4 * 1/2 = 17/8.
Now, let's express 17/8 as a mixed number.
Dividing 17 by 8: 17 ÷ 8 = 2 with a remainder of 1.
Therefore, the rational number between 2 and 2 1/4, found by adding the numbers together and dividing by 2, is 2 1/8.
Converting 2 1/4 to an improper fraction: 2 1/4 = 9/4.
Sum of the numbers: 2 + 9/4 = 8/4 + 9/4 = 17/4.
Dividing the sum by 2: (17/4) ÷ 2 = 17/4 ÷ 2/1.
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction: 17/4 ÷ 2/1 = 17/4 * 1/2.
Multiplying the fractions: 17/4 * 1/2 = 17/8.
Now, let's express 17/8 as a mixed number.
Dividing 17 by 8: 17 ÷ 8 = 2 with a remainder of 1.
Therefore, the rational number between 2 and 2 1/4, found by adding the numbers together and dividing by 2, is 2 1/8.
Find a rational number with one decimal place that is between √17 and √18
To find a rational number with one decimal place between √17 and √18, we can add the numbers together and divide by 2.
√17 ≈ 4.123105625617661
√18 ≈ 4.242640687119285
Sum of the numbers: 4.123105625617661 + 4.242640687119285 = 8.365746312736946
Dividing the sum by 2: 8.365746312736946 ÷ 2 ≈ 4.182873156368473
Therefore, a rational number with one decimal place between √17 and √18 is approximately 4.2.
√17 ≈ 4.123105625617661
√18 ≈ 4.242640687119285
Sum of the numbers: 4.123105625617661 + 4.242640687119285 = 8.365746312736946
Dividing the sum by 2: 8.365746312736946 ÷ 2 ≈ 4.182873156368473
Therefore, a rational number with one decimal place between √17 and √18 is approximately 4.2.
Which of the following is between and ?(1 point)
Responses
Start Root 8 End Root
Start Root 10 End Root
Start Root 12 End Root
Responses
Start Root 8 End Root
Start Root 10 End Root
Start Root 12 End Root
To determine which of the given options is between √8 and √10, we can calculate the approximate values of each option.
Starting with √8 and √10:
√8 ≈ 2.8284271247461903
√10 ≈ 3.1622776601683795
Checking each option:
Option 1: Start Root 8 End Root ≈ 2.8284271247461903
Option 2: Start Root 10 End Root ≈ 3.1622776601683795
Option 3: Start Root 12 End Root
Comparing the values:
2.8284271247461903 < 3.1622776601683795
Therefore, the option between √8 and √10 is Option 2: Start Root 10 End Root.
Starting with √8 and √10:
√8 ≈ 2.8284271247461903
√10 ≈ 3.1622776601683795
Checking each option:
Option 1: Start Root 8 End Root ≈ 2.8284271247461903
Option 2: Start Root 10 End Root ≈ 3.1622776601683795
Option 3: Start Root 12 End Root
Comparing the values:
2.8284271247461903 < 3.1622776601683795
Therefore, the option between √8 and √10 is Option 2: Start Root 10 End Root.
√ Show an example of an irrational number between 9 and 11.(1 point)
Responses
start root 10 end root
start root 100 end root
start root 99 end root
start root 20 end root
Responses
start root 10 end root
start root 100 end root
start root 99 end root
start root 20 end root
An example of an irrational number between 9 and 11 is √10.
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
25
25
26
26
6
6
13
Responses
25
25
26
26
6
6
13
To find the least integer whose square root is an irrational number between 5 and 7, we need to calculate the square root of each option and determine if it is irrational.
Calculating the square root of each option:
√25 = 5
√26 ≈ 5.099
√6 ≈ 2.449
√13 ≈ 3.605
Checking if the square root is irrational:
The only option with an irrational square root between 5 and 7 is √26.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 26
Calculating the square root of each option:
√25 = 5
√26 ≈ 5.099
√6 ≈ 2.449
√13 ≈ 3.605
Checking if the square root is irrational:
The only option with an irrational square root between 5 and 7 is √26.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 26
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
25
25
26
26
6
6
13
Responses
25
25
26
26
6
6
13
Apologies for the incorrect response earlier. Let's go through the options again.
Calculating the square root of each option:
√25 = 5
√26 ≈ 5.099
√6 ≈ 2.449
√13 ≈ 3.605
Checking if the square root is irrational:
The only option with an irrational square root between 5 and 7 is √26.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 26.
Calculating the square root of each option:
√25 = 5
√26 ≈ 5.099
√6 ≈ 2.449
√13 ≈ 3.605
Checking if the square root is irrational:
The only option with an irrational square root between 5 and 7 is √26.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 26.
Show an example of a rational number that is between √10 and √ 11 .(1 point)
Responses
Start Fraction 10 over 3 end fraction
3.1
3.1
Start Fraction 16 over 5 end fraction
3.4
Responses
Start Fraction 10 over 3 end fraction
3.1
3.1
Start Fraction 16 over 5 end fraction
3.4
An example of a rational number that is between √10 and √11 is 3.4.
Which irrational number is between √14 and √18 ?(1 point)
Responses
start root 13 end root
start root 10 end root
start root 19 end root
Responses
start root 13 end root
start root 10 end root
start root 19 end root
The irrational number between √14 and √18 is √16.
Which irrational number is between √14 and √18 ?(1 point)
Responses
start root 13 end root
start root 10 end root
start root 19 end root
start root 15 end root
Responses
start root 13 end root
start root 10 end root
start root 19 end root
start root 15 end root
The irrational number between √14 and √18 is √16.
How many irrational numbers are there between √11 and √17 ?(1 point)
Responses
four numbers
four numbers
an infinite number
an infinite number
twenty-eight numbers
twenty-eight numbers
six numbers
Responses
four numbers
four numbers
an infinite number
an infinite number
twenty-eight numbers
twenty-eight numbers
six numbers
To determine how many irrational numbers there are between √11 and √17, we need to calculate the square roots of 11 and 17 and count the irrational numbers between them.
Calculating the square roots:
√11 ≈ 3.316
√17 ≈ 4.123
Based on the given values, there are an infinite number of irrational numbers between √11 and √17.
Therefore, the correct response is: an infinite number.
Calculating the square roots:
√11 ≈ 3.316
√17 ≈ 4.123
Based on the given values, there are an infinite number of irrational numbers between √11 and √17.
Therefore, the correct response is: an infinite number.