Question

HELP PLEASE! Thanks :)

1. Select all irrational numbers.



10−−√
27−−√
49−−√
64−−√
99−−√



2. Select all irrational numbers.



316−−√
416−−√
916−−√
34√
94√


3. Select all numbers that are irrational.



144−−−√
π
0.45
8√

Answer 1

The formatting on this question is rather poor. I am going to assume that 10â’â’âš actually means square root of 10. And will assume that for the other options of the same style. And in fact all of the options for all of the questions here are the square root of some number except for the options of Ď€ and 0.45. With that in mind, review what an rational number is. A rational number is any number that can be represented as a fraction with integer numerator and divisor. 1. sqrt(10) * This is an irrational number. Sqrt(10) = sqrt(2)*sqrt(5) and you should have been told time and time again, that sqrt(2) is irrational. But also sqrt(5) is irrational as well. sqrt(27) Irrational sqrt(49) Rational. Value is 7 which can be represented as 7/1 sqrt(64) Rational. Value is 8 which can be represented as 8/1 sqrt(99) Irrational 2. sqrt(316) Irrational sqrt(416) Irrational sqrt(916) Irrational sqrt(34) Irrational sqrt(94) Irrational 3. sqrt(144) Rational. Value is 12 which can be represented as 12/1 Ď€ Irrational. Pi is a non repeating, non terminating value. 0.45 Rational. Can be represented as 9/20 sqrt(8) Irrational.

Answer 2

Answer: The irrational numbers are in 1. √10,√27,√99

In 2. √316, √416, √916 √34 √94

In 3.
`\pi`, √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),

`\pi` , √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.