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Ответ:

Let's simplify each of these expressions step by step:

a) √3 (√27 + 0.4√75):

First, let's simplify the square roots:

√27 = √(9 * 3) = 3√3

√75 = √(25 * 3) = 5√3

Now, we can rewrite the expression:

√3 (3√3 + 0.4 * 5√3)

Next, distribute the √3 into the parentheses:

3√3 * √3 + 0.4 * 5√3 * √3

Now, multiply the terms inside the square roots:

3 * 3 + 0.4 * 5 * 3

Simplify further:

9 + 6

Combine like terms:

15

So, the simplified expression is 15.

   (√20 - 6√5 + √45)√5:

Let's simplify the square roots first:

√20 = √(4 * 5) = 2√5

√45 = √(9 * 5) = 3√5

Now, rewrite the expression:

(2√5 - 6√5 + 3√5)√5

Now, combine like terms inside the parentheses:

(2√5 - 6√5 + 3√5)√5 = (-1√5)√5

Multiplying the square roots:

-1 * 5 = -5

So, the simplified expression is -5.

г) (√15 - √6)² + (√3 + √30)²:

Let's simplify each square separately:

(√15 - √6)²:

Expand this using the formula (a - b)² = a² - 2ab + b²:

(√15)² - 2(√15)(√6) + (√6)²

15 - 2√(15 * 6) + 6

(√3 + √30)²:

Expand using the same formula:

(√3)² + 2(√3)(√30) + (√30)²

3 + 2√(3 * 30) + 30

Now, add the two simplified squares together:

(15 - 2√90 + 6) + (3 + 2√90 + 30)

Combine like terms:

(15 + 6 + 3) + (-2√90 + 2√90) + 30

Simplify further:

24 + 0 + 30

So, the simplified expression is 54.

B) (2√8 + 3√5 - 7√2)(2√2 + 2√5):

First, simplify the square roots:

√8 = √(4 * 2) = 2√2

√5 = √5

Now, rewrite the expression:

(2√2 + 3√5 - 7√2)(2√2 + 2√5)

Now, distribute and multiply the terms:

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

Simplify each term:

4 * 2 + 4√10 + 6√10 + 6 * 5 - 14 * 2√2 - 14 * 2√5

Now, combine like terms:

8 + 10√10 + 30 - 28√2 - 28√5

Combine the constants:

(8 + 30) + (-28√2 - 28√5) + 10√10

38 - 28(√2 + √5) + 10√10

So, the simplified expression is 38 - 28(√2 + √5) + 10√10.

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