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Question
`6/sqrt(2), sqrt(8), 4sqrt(2)` in ascending order is ______.
Options
`4sqrt(2), sqrt(8), 6/sqrt(2)`
`sqrt(8), 6/sqrt(2), 4sqrt(2)`
`6/sqrt(2), 4sqrt(2), sqrt(8)`
`sqrt(8), 4sqrt(2), 6/sqrt(2)`
MCQ
Fill in the Blanks
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Solution
`6/sqrt(2), sqrt(8), 4sqrt(2)` in ascending order is `underlinebb(sqrt(8), 6/sqrt(2), 4sqrt(2))`.
Explanation:
Step 1: Simplify each expression
1. `6/sqrt(2)`
= `6/sqrt(2) xx sqrt(2)/sqrt(2)`
= `(6sqrt(2))/2`
= `3sqrt(2)`
2. `sqrt(8)`
= `sqrt(4 xx 2)`
= `2sqrt(2)`
3. Remains as is `4sqrt(2)`
Step 2: Compare coefficients of `sqrt(2)`
- `sqrt(8) = 2sqrt(2)`
- `6/sqrt(2) = 3sqrt(2)`
- `4sqrt(2)`
Clearly, `2sqrt(2) < 3sqrt(2) < 4sqrt(2)`
Step 3: Rewrite in original form
`sqrt(8) < 6/sqrt(2) < 4sqrt(2)`
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