# How do you solve #5sqrt 18 - sqrt 28 + sqrt 63 - sqrt 8#?

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To solve 5sqrt(18) - sqrt(28) + sqrt(63) - sqrt(8), first simplify the square roots:

sqrt(18) = sqrt(9 * 2) = 3sqrt(2) sqrt(28) = sqrt(4 * 7) = 2sqrt(7) sqrt(63) = sqrt(9 * 7) = 3sqrt(7) sqrt(8) = sqrt(4 * 2) = 2sqrt(2)

Now, substitute the simplified expressions back into the original expression:

5 * 3sqrt(2) - 2sqrt(7) + 3sqrt(7) - 2 * 2sqrt(2)

Now, combine like terms:

= 15sqrt(2) - 2sqrt(7) + 3sqrt(7) - 4sqrt(2)

= (15sqrt(2) - 4sqrt(2)) + (-2sqrt(7) + 3sqrt(7))

= 11sqrt(2) + sqrt(7)

So, 5sqrt(18) - sqrt(28) + sqrt(63) - sqrt(8) simplifies to 11sqrt(2) + sqrt(7).

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