Answer: The irrational numbers are in 1. √10,√27,√99
In 2. √316, √416, √916 √34 √94
In 3. [tex]\pi[/tex], √8
Explanation: Since, according to the property of irrational number .
The number which can not be written in the form of p/q where q≠0 is called irrational number.
And, the number after the product of a rational number and an irrational number or after the product of two irrational numbers always an irrational number.
In option (1) √10 = √2×√5 Since, both √2 and √5 are irrational numbers.
So, √10 is an irrational.
√27=3√3, where 3 is rational but √3 is irrational.
⇒√27 is an irrational number.
√99=3√11, where 3 is rational but √11 is irrational.
⇒√99 is irrational.
But, √49=7 and √64=8 both are rational because 7 and 8 are integers. And, an integer is always a rational number.
In option (2) √316=2√79, where 2 is rational but √79 is irrational.
⇒√316 is irrational.
Similarly, we can say √416, √916, √34 and √94 are irrational because they are also the product of rational and irrational numbers.
In option (3),
[tex]\pi[/tex] , √8 are also irrational numbers because we can not write them in form of p/q.
While √144=12 and .45=45/100 are rational numbers.
