Question

3√8+√2-3√18 (√5-√2)^{2} (2-√3)(2+√3)

Answer 1

1) = 3 корень из 4 * 2 + корень из 2 - 3 корень из 9 * 3 = 6 корень из 2 + корень из 2 - 9 корень из 2 = -2 корень из 2
2) = (корень из 5)^{2} - (корень из 2)^{2} = 5-2=3
3) = (2)^{2} - (корень из 3)^{2} = 4 - 3 = 1

Answer 2

Let's break down this expression step by step.

First, we can simplify the cube root expressions:

• 3√8 = 3 * √(2^3) = 3 * 2√2 = 6√2
• 3√18 = 3 * √(2 * 3^2) = 3 * 3√2 = 9√2

So the expression becomes:

6√2 + √2 - 9√2 (√5 - √2)^2 (2 - √3)(2 + √3)

Next, we can simplify the square of the binomial (√5 - √2)^2:

(√5 - √2)^2 = (√5)^2 - 2 * √5 * √2 + (√2)^2 = 5 - 2√10 + 2 = 7 - 2√10

So the expression becomes:

6√2 + √2 - 9√2 (7 - 2√10) (2 - √3)(2 + √3)

Next, we can simplify the expression inside the parentheses (2 - √3)(2 + √3) using the difference of squares formula:

(2 - √3)(2 + √3) = 2^2 - (√3)^2 = 4 - 3 = 1

So the expression becomes:

6√2 + √2 - 9√2 (7 - 2√10) * 1

Finally, we can simplify the expression in the parentheses:

• 9√2 (7 - 2√10) = 63√2 - 18√20
• 18√20 = 18 * √(2 * 2^2 * 5) = 36√5

So the final result is:

6√2 + √2 - 63√2 + 36√5 = -56√2 + 36√5

Therefore, the answer is -56√2 + 36√5.