Question

Select all irrational numbers.

4√
8√
10−−√
15−−√
36−−√

Answer 1

√8, √10, √15

Explanation:

An irrational number can not be written in the form of
`(p)/(q)`,

Where,

p and q are integers,

Such that q ≠ 0,

Also, a prime number inside square root is always an irrational number.

And, when we multiply an irrational number by a rational number the resultant number is also irrational.

While, when we multiply two different irrational numbers the result is also irrational.

∵ √4 = 2 =
`(2)/(1)` where, 2 and 1 are integers s. t. 1 ≠ 0,

⇒ √4 is not irrational.

√8 = 2 × √2 = product of rational number and irrational number

⇒ √8 is irrational,

√10 = √5 × √2 = product of two different irrational numbers

⇒ √10 is irrational,

√15 = √3 × √5 = product of two different irrational numbers

⇒ √15 is irrational,

√36 = 4,

⇒ √36 is not irrational.

Answer 2

sqrt (4) =2 rational

sqrt (8) = 2sqrt(2) = irrational

sqrt (10)= irrational

sqrt(15) irrational

sqrt(36) =6 rational