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Question
Simplify the following:
`sqrt(147) - sqrt(27) + sqrt(75) - sqrt(48)`
Simplify
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Solution
`sqrt(147) - sqrt(27) + sqrt(75) - sqrt(48)`
Step 1: Break each term into factors of perfect squares
`sqrt(147) = sqrt(49.3) = 7sqrt(3)`
`sqrt(27) = sqrt(9.3) = 3sqrt(3)`
`sqrt(75) = sqrt(25 xx 3) = 5sqrt(3)`
`sqrt(48) = sqrt(16 xx 3) = 4sqrt(3)`
Step 2: Substitute back
`sqrt(147) - sqrt(27) + sqrt(75) - sqrt(48)`
= `7sqrt(3) - 3sqrt(3) + 5sqrt(3) - 4sqrt(3)`
Step 3: Combine like terms
`(7 - 3 + 5 - 4)sqrt(3) = 5sqrt(3)`
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