Question

3√x+2√y+9√x √18×(√16-√10+2√20)

Answer 1

Ответ:

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Answer 2

Let's simplify the expression step by step:

1. Start with the expression:

   3√x + 2√y + 9√x √18 × (√16 - √10 + 2√20)

2. Simplify the square roots and constants inside the square root:

   3√x + 2√y + 9√x √(9 * 2) × (√(4^2) - √10 + 2√(4 * 5))

   Now, simplify the square roots inside the square root:

   3√x + 2√y + 9√x √(3^2 * 2) × (√(4^2) - √10 + 2√(4 * 5))

3. Further simplify the expression inside the square root:

   3√x + 2√y + 9√x √(3^2) √2 × (√(4^2) - √10 + 2√(4 * 5))

   3√x + 2√y + 9√x * 3 * √2 × (√(4^2) - √10 + 2√(4 * 5))

4. Simplify the constants outside the square root:

   3√x + 2√y + 27√(2x) × (√(4^2) - √10 + 2√(4 * 5))

5. Simplify the square roots inside the square root:

   3√x + 2√y + 27√(2x) × (4 - √10 + 2√(4 * 5))

6. Calculate the values inside the parentheses:

   3√x + 2√y + 27√(2x) × (4 - √10 + 2√20)

7. Multiply each term by the expression inside the parentheses:

   (3√x) * (4 - √10 + 2√20) + (2√y) * (4 - √10 + 2√20) + (27√(2x)) * (4 - √10 + 2√20)

Now, distribute and simplify each term:

8. Distribute and simplify:

   (3√x) * 4 - (3√x) * √10 + (3√x) * 2√20 + (2√y) * 4 - (2√y) * √10 + (2√y) * 2√20 + (27√(2x)) * 4 - (27√(2x)) * √10 + (27√(2x)) * 2√20

9. Further simplify:

   12√x - 3√(10x) + 6√(20x) + 8√y - 2√(10y) + 4√(20y) + 108√(2x) - 27√(10x) + 54√(40x)

10. Combine like terms:

(12√x + 8√y + 108√(2x)) - (3√(10x) + 2√(10y) + 27√(10x)) + (6√(20x) + 4√(20y) + 54√(40x))

11. Further simplify:

12√x + 8√y + 108√(2x) - 3√(10x) - 2√(10y) - 27√(10x) + 6√(20x) + 4√(20y) + 54√(40x)

That's the simplified expression. You can factor out common terms or perform any additional simplifications if needed.