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Question
Which of the following is an irrational number?
Options
`sqrt(8) xx sqrt(50)`
`sqrt(48)/sqrt(27)`
`sqrt(75)`
`(sqrt(18) + sqrt(8))^2`
MCQ
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Solution
`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)
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