Question

0,125¯1 * (5 корень 4 * 5 корень 8)¯2​

Answer 1

Ответ:

1/2500

Пошаговое объяснение:

0,125^-1= 1000/125

(5√4*5√8)^-2= 1/(10*10√2)^2= 1/20000

теперь объединим :

1000/125*1/20000=1/2500

Answer 2

Ответ:

Пошаговое объяснение:

1/2000

Answer 3

To simplify the expression, let's first deal with the numbers under the radicals.

The expression (5√4 * 5√8)² can be simplified as follows:

1. 5√4 = 5 * √4 = 5 * 2 = 10
2. 5√8 = 5 * √8 = 5 * √(4 * 2) = 5 * 2√2 ≈ 5 * 2.83 ≈ 14.14
3. (10 * 14.14)² = 141.4² ≈ 19992.96

Now, let's handle the repeating decimal (125¯1) which means 125.111... with the 1's repeating infinitely.

To express this repeating decimal as a fraction, we can call it x: x = 125.111... 10x = 1251.111... Subtract the equation above from the one below: 10x - x = 1251.111... - 125.111... 9x = 1126 x = 1126 / 9 x ≈ 125.1111...

Now, the original expression becomes:

0.125¯1 * (5√4 * 5√8)²

≈ (1126 / 9) * (19992.96)

To multiply these two numbers, we get:

≈ 1126 * 19992.96 / 9

≈ 22513,696 / 9

Now, let's divide 22513.696 by 9:

22513.696 / 9 ≈ 2501.521777778

So, the simplified result of the expression is approximately 2501.521777778.