Show an example of an irrational number between 9 and 11.(1 point)
Responses
20−−√
start root 20 end root
100−−−√
start root 100 end root
99−−√
start root 99 end root
10−−√
start root 10 end root
are u sure
I apologize for the incorrect response. You are right, √10 is not an irrational number between 9 and 11. To provide an example of an irrational number between 9 and 11, I can use π (pi) which is approximately 3.14159.
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
a. 25
b. 6
c.13
d. 26
To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest perfect square greater than 25 (5^2) and 49 (7^2).
The option that satisfies this condition is:
d. 26
Because 26 is the smallest perfect square greater than 25, its square root (√26) is an irrational number between 5 and 7.
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
a. 3.4
b. 165
Start Fraction 16 over 5 end fraction
c. 103
Start Fraction 10 over 3 end fraction
d. 3.1
To find a rational number between √10 and √11, we can simplify the options provided:
a. 3.4 is not a rational number.
b. Start Fraction 16 over 5 end fraction is a rational number, but it is not between √10 and √11.
c. Start Fraction 10 over 3 end fraction is a rational number, but it is not between √10 and √11.
d. 3.1 is not a rational number.
None of the given options is a rational number between √10 and √11.
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
a. 3.4
b. 16/5
c. 10/3
d. 3.1
To find a rational number between √10 and √11, we can simplify the options provided:
a. 3.4 is not a rational number.
b. 16/5 is a rational number but it is not between √10 and √11.
c. 10/3 is a rational number but it is not between √10 and √11.
d. 3.1 is not a rational number.
None of the given options is a rational number between √10 and √11.
However, we can find a rational number between √10 and √11 by rationalizing the denominator of one of these square roots.
Let's rationalize the denominator of √10:
√10 = (√10 * (√10))/(√10) = √100/√10 = 10/√10 = (10/√10) * (√10/√10) = (10√10)/10 = √10
Therefore, √10 is a rational number and it lies between itself and √11.
Which irrational number is between 14−−√ and 18−−√?(1 point)
Responses
19−−√
start root 19 end root
10−−√
start root 10 end root
15−−√
start root 15 end root
13−−√