Question

Which of the following is an irrational number?

विकल्प

• `sqrt(8) xx sqrt(50)`

• `sqrt(48)/sqrt(27)`

• `sqrt(75)`

• `(sqrt(18) + sqrt(8))^2`

Answer 1

`bb(sqrt(75))`

Explanation:

a. `sqrt(8) xx sqrt(50)`

Use the property:

`sqrt(a) xx sqrt(b) = sqrt(a xx b)`

`sqrt(8 xx 50) = sqrt(400) = 20`  ...(rational)

b. `sqrt(48)/sqrt(27)`

= `sqrt(48/27)`

= `sqrt(16/9)`

= `4/3`  ...(rational)

c. `sqrt(75)`

= `sqrt(25 xx 3)`

= `5sqrt(3)`  ...(irrational)

d. `(sqrt(18) + sqrt(8))^2`

First simplify:

`sqrt(18) = 3sqrt(2), sqrt(8) = 2sqrt(2)`

`(sqrt(18) + sqrt(8))^2 = (3sqrt(2) + 2sqrt(2))^2`

= `(5sqrt(2))^2`

= 25 × 2

= 50  ...(rational)