Question

(3√6 + 2√8 - √32 )*√2 -√108 помогите решить поэтапно

Answer 1

Решение смотри внизу

Answer 2

(3√6+4√2-4√2)√2-6√3
3√6*√2-6√3
3√12-6√3
6√3-6√3=0

Answer 3

Sure, I can help you solve the expression step-by-step. Let's start by simplifying each square root term:

Step 1: Simplify the square root terms. We have:

• √6
• √8
• √32

To simplify these square roots, we look for perfect squares that are factors of the numbers under the square roots:

√6 = √(2 * 3) = √2 * √3 √8 = √(2 * 4) = √2 * √4 = √2 * 2 = 2√2 √32 = √(2 * 16) = √2 * √16 = √2 * 4 = 4√2

So, the expression becomes:

(√2 * √3 + 2√2 - 4√2) * √2 - √108

Step 2: Combine like terms. Combine the terms with the same square root expression:

(√2 - √2) * √2 - √108

The (√2 - √2) term simplifies to zero, so we are left with:

0 * √2 - √108

Step 3: Perform arithmetic. 0 times any number is zero, so we have:

0 - √108

Step 4: Simplify the remaining square root term. √108 is not a perfect square, but it has a perfect square factor. Let's find it:

√108 = √(2 * 54) = √(2 * 2 * 27) = 2√27

Now, let's find the perfect square factor of 27:

√27 = √(3 * 9) = √(3 * 3 * 3) = 3√3

So, the expression becomes:

-2√3

That's the final simplified result. The expression (3√6 + 2√8 - √32) * √2 - √108 simplifies to -2√3.