Question

УПРОСТИТЕ ВЫРАЖЕНИЕ (5√2-7√3)√6 (3√5-2√3)√5+√60 (√50+√10)√10 (√m-√n)^2 (√5-√2)^2 (5√5+3√3)√45 решите срочно надо пжл кто решит дам ссылку где еще по 80 балллов есть

Answer 1

(5√2 - 7√3)√6 = 5√12 - 7√18 = 10√3 - 21√2
(3√5-2√3)√5+√60 =3√25 -2√15 + 2√15 = 15
(√50+√10)√10=√500 + √100 = 10√5 + 10
(√m-√n)^2 = m -2√(mn) + n
(√5-√2)^2 = 5 - 2√10 + 2 = 7 - 2√10
(5√5+3√3)√45= 5√225 + 3√135 = 75 - 9√15

Answer 2

Simplifying the Expression

To simplify the given expression, let's break it down step by step.

The given expression is: (5√2-7√3)√6 + (3√5-2√3)√5 + √60 + (√50+√10)√10 + (√m-√n)^2 + (√5-√2)^2 + (5√5+3√3)√45

First, let's simplify each part of the expression separately.

1. Simplify (5√2-7√3)√6: - Multiply each term inside the parentheses by √6. - This simplifies to 30√2 - 42√3.

2. Simplify (3√5-2√3)√5: - Multiply each term inside the parentheses by √5. - This simplifies to 15√5 - 10√3.

3. Simplify √60: - √60 simplifies to 2√15.

4. Simplify (√50+√10)√10: - Multiply each term inside the parentheses by √10. - This simplifies to 10√50 + 10√10.

5. Simplify (√m-√n)^2: - This is a binomial squared, which simplifies to m - 2√mn + n.

6. Simplify (√5-√2)^2: - This is also a binomial squared, which simplifies to 5 - 2√10 + 2.

7. Simplify (5√5+3√3)√45: - Multiply each term inside the parentheses by √45. - This simplifies to 225√5 + 135√3.

Now, let's combine all the simplified parts of the expression.

The simplified expression is: (30√2 - 42√3) + (15√5 - 10√3) + 2√15 + (10√50 + 10√10) + (m - 2√mn + n) + (5 - 2√10 + 2) + (225√5 + 135√3)

Final Simplified Expression

The final simplified expression is: m - 2√mn + n + 30√2 - 52√3 + 15√5 + 2√15 + 10√50 + 10√10 + 5 - 2√10 + 225√5 + 135√3

This is the simplified form of the given expression.

If you need further assistance or have any other questions, feel free to ask!