Question

√(8-6√8+9) +2√2 как решить?подробно

Answer 1

$\tt{} \ \ \ \sqrt{8-6\sqrt{8}+9}+2\sqrt{2}= \sqrt{(\sqrt{8})^2-2\cdot\sqrt{8}\cdot3+3^2}+2\sqrt{2} =\\\\=\sqrt{(\sqrt{8}-3)^2}+2\sqrt{2} =|\sqrt{8}-3|+2\sqrt{2}=3-\sqrt{8}+2\sqrt{2}=\\\\=3-2\sqrt{2}+2\sqrt{2}=3$

Answer 2

$\sqrt{(8 - 6 \sqrt{8} + 9) } + 2 \sqrt{2}$

$\sqrt{( \sqrt{8} - 3)^{2} } + 2 \sqrt{2}$

$3 - \sqrt{8} + 2 \sqrt{2}$

$3 - 2 \sqrt{2} + 2 \sqrt{2}$

$3$

Answer 3

To simplify the expression √(8 - 6√8 + 9) + 2√2, follow these steps:

Step 1: Simplify the expression inside the square root (√) as much as possible. Step 2: Combine like terms inside the square root. Step 3: Calculate the square root of the simplified expression. Step 4: Add 2√2 to the result from Step 3.

Let's begin:

Step 1: Simplify the expression inside the square root (√). The expression inside the square root is 8 - 6√8 + 9.

Step 2: Combine like terms inside the square root. The terms that contain √8 are like terms: -6√8 and 8√8.

8 - 6√8 + 9 can be written as (8 + 9) - 6√8, which simplifies to 17 - 6√8.

Step 3: Calculate the square root of the simplified expression. √(17 - 6√8)

Step 4: Add 2√2 to the result from Step 3. √(17 - 6√8) + 2√2

Unfortunately, this expression cannot be simplified further without knowing the exact value of √8. However, you can approximate the result using a calculator. If you provide the approximate value of √8 (usually rounded to several decimal places), I can help you further.