Question

(4(sqrt2/5)+1/3(sqrt90)-6sqrt(0.1))*sqrt10

Answer 1

Ответ:

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Пошаговое объяснение:

Answer 2

Let's simplify the expression step by step:

1. First, let's simplify the individual terms inside the parentheses:

   a. 4(√2/5) To simplify this, multiply 4 with (√2/5): 4 * (√2/5) = (4√2) / 5

   b. 1/3(√90) To simplify this, multiply 1/3 with (√90): (1/3) * (√90) = (√90) / 3

2. Now, let's rewrite the expression with the simplified terms: (4√2 / 5) + (√90 / 3) - 6√(0.1)

3. Next, let's simplify √90 and √(0.1):

   a. √90 = √(9 * 10) = √9 * √10 = 3 * √10

   b. √(0.1) = √(1/10) = √1 / √10 = 1 / √10

4. Substitute the simplified values into the expression: (4√2 / 5) + (3√10 / 3) - 6 * (1 / √10)

5. Further simplification:

   a. 3√10 / 3 simplifies to √10.

   b. 6 * (1 / √10) = 6 / √10. To rationalize the denominator, we multiply both the numerator and the denominator by √10: (6 / √10) * (√10 / √10) = 6√10 / 10.

6. Rewrite the expression with the further simplified terms: (4√2 / 5) + √10 - (6√10 / 10)

7. Now, let's find a common denominator for the terms with radicals (5 and 10):

   a. The term with √2/5 already has a denominator of 5, so it's good as it is.

   b. To make the second term √10 have a denominator of 10, multiply it by 2/2: √10 = (√10 * 2) / 2 = (2√10) / 2 = √10.

8. Rewrite the expression with the common denominator: (4√2 / 5) + (2√10 / 2) - (6√10 / 10)

9. Combine like terms: The terms with √10 can be combined now: (4√2 / 5) + (√10 - 6√10 / 10)

10. Subtract the fractions with √10: To subtract the fractions, they need to have a common denominator, which is 10. The second fraction needs to be multiplied by 5/5 to achieve this: (4√2 / 5) + (10√10 - 6√10) / 10

11. Combine like terms: 10√10 - 6√10 = 4√10 (4√2 / 5) + (4√10 / 10)

12. Find the common denominator for the terms: The first term 4√2 / 5 already has a denominator of 5, so no further changes are needed.

To make the second term 4√10 / 10 have a denominator of 5, multiply it by 2/2: (4√10 / 10) * (2 / 2) = (8√10) / 20

13. Combine like terms: (4√2 / 5) + (8√10 / 20)

14. Now, find a common denominator for the terms: The first term 4√2 / 5 already has a denominator of 5, so no further changes are needed.

To make the second term 8√10 / 20 have a denominator of 5, multiply it by 1/4: (8√10 / 20) * (1 / 4) = (2√10) / 5

15. Final simplified expression: (4√2 / 5) + (2√10 / 5)

So, the simplified expression is (4√2 / 5) + (2√10 / 5).