Which irrational number is between 14−−√ and 18−−√?(1 point)
Responses
15−−√
start root 15 end root
13−−√
start root 13 end root
19−−√
start root 19 end root
10−−√
start root 10 end root
15−−√
To find an irrational number between √14 and √18, we can find the average of the two numbers.
The average of √14 and √18 is (√14 + √18)/2.
Simplifying this expression, we get (√(2*7) + √(2*9))/2.
Taking out the common factor of 2 from each square root, we have (2√7 + 3√2)/2.
Finally, simplifying further, we get √7/2 + (3√2)/2.
Therefore, an irrational number between √14 and √18 is (√7 + 3√2)/2.