Sqrt(88-30 sqrt 7)-3 sqrt 7

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вопрос

To simplify the expression, we first need to remember that sqrt(a b) = sqrt(a) sqrt(b).

Given expression: sqrt(88 - 30sqrt(7)) - 3sqrt(7)

Now, let's break down the expression further:

sqrt(88 - 30sqrt(7)) = sqrt(4 22 - 30sqrt(7))
= sqrt(4) sqrt(22) - sqrt(4) sqrt(30) sqrt(7)
= 2sqrt(22) - 2sqrt(30)sqrt(7)
= 2sqrt(22) - 2sqrt(210)
= 2sqrt(22) - 2sqrt(2 105)
= 2sqrt(22) - 2sqrt(2) sqrt(105)
= 2sqrt(22) - 2sqrt(2) * 5sqrt(7)
= 2sqrt(22) - 10sqrt(14)

Now, we substitute the simplified value back into the original expression:

2sqrt(22) - 10sqrt(14) - 3sqrt(7)
= 2sqrt(22) - 10sqrt(14) - 3sqrt(7)

Thus, the simplified form of the expression sqrt(88 - 30sqrt(7)) - 3sqrt(7) is 2sqrt(22) - 10sqrt(14) - 3sqrt(7).