Question

(3√5-5√3)²=? (√14+√8)²=? Подробное решение, пожалуйста

Answer 1

1.(3√5-5√3)²=9*5-30√5*√3+25*3=45-30√15+75=120-30√15
2.(√14+√8)²=14+2√14*√8+8=22+2√112

Answer 2

Calculation 1: (3√5-5√3)²

To calculate the expression (3√5-5√3)², we can use the formula for squaring a binomial:

Formula: (a - b)² = a² - 2ab + b²

In this case, a = 3√5 and b = 5√3. Let's substitute these values into the formula:

(3√5 - 5√3)² = (3√5)² - 2(3√5)(5√3) + (5√3)²

Simplifying further:

(3√5 - 5√3)² = 9(√5)² - 30√5√3 + 25(√3)²

Since (√a)² = a, we can simplify the expression:

(3√5 - 5√3)² = 9(5) - 30√15 + 25(3)

Calculating the values:

(3√5 - 5√3)² = 45 - 30√15 + 75

(3√5 - 5√3)² = 120 - 30√15

Therefore, (3√5 - 5√3)² is equal to 120 - 30√15.

Calculation 2: (√14 + √8)²

To calculate the expression (√14 + √8)², we can again use the formula for squaring a binomial:

Formula: (a + b)² = a² + 2ab + b²

In this case, a = √14 and b = √8. Let's substitute these values into the formula:

(√14 + √8)² = (√14)² + 2(√14)(√8) + (√8)²

Simplifying further:

(√14 + √8)² = 14 + 2√14√8 + 8

Since (√a)² = a, we can simplify the expression:

(√14 + √8)² = 14 + 2√(14*8) + 8

Calculating the values:

(√14 + √8)² = 14 + 2√112 + 8

(√14 + √8)² = 22 + 2√112

Therefore, (√14 + √8)² is equal to 22 + 2√112.

I hope this helps! Let me know if you have any further questions.