Question

Надо вычислить:(3√15)^2/15= 2√6*√2*8√3= (√19-4)(√19+4)=

Answer 1

1) (3√15)²÷15=9×15÷15=9.
2) 2√6×√2×8√3=16√36=16×6=96
3) (√19-4)×(√19+4)=19-16=3

Answer 2

Let's break down the calculations step by step:

1. (3√15)^2 / 15: First, simplify the expression inside the parentheses: (3√15)^2 = 9 * √15 * √15 = 9 * 15 = 135 Now, divide by 15: (3√15)^2 / 15 = 135 / 15 = 9

2. 2√6 * √2 * 8√3: Multiply the coefficients: 2 * 8 = 16 Multiply the square roots: √6 * √2 * √3 = √(6 * 2 * 3) = √36 = 6 Therefore, 2√6 * √2 * 8√3 = 16 * 6 = 96

3. (√19 - 4) * (√19 + 4): This is a difference of squares, (a^2 - b^2) = (a + b)(a - b) So in this case, a = √19 and b = 4: (√19 - 4) * (√19 + 4) = (√19)^2 - (4)^2 = 19 - 16 = 3

To summarize the calculations:

1. (3√15)^2 / 15 = 9
2. 2√6 * √2 * 8√3 = 96
3. (√19 - 4) * (√19 + 4) = 3