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Question
`sqrt(2)(sqrt(8) + sqrt(18))` when simplified becomes ______.
Options
`2sqrt(7)`
10
`sqrt(52)`
8
MCQ
Fill in the Blanks
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Solution
`sqrt(2)(sqrt(8) + sqrt(18))` when simplified becomes 10.
Explanation:
We need to simplify:
`sqrt(2)(sqrt(8) + sqrt(18))`
Step 1: Simplify inside the parentheses
`sqrt(8)`
= `sqrt(4 xx 2)`
= `2sqrt(2)`
`sqrt(18)`
= `sqrt(9 xx 2)`
= `3sqrt(2)`
So, `sqrt(8) + sqrt(18)`
= `2sqrt(2) + 3sqrt(2)`
= `5sqrt(2)`
Step 2: Multiply by `sqrt(2)`
`sqrt(2) xx 5sqrt(2)`
= `5(sqrt(2) xx sqrt(2))`
= 5 × 2
= 10
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