Question

Звільніть віл іпраціональномті в знамееику дробу 12/✓7-1

Answer 1

Ответ:

2(√7+1)

Пошаговое объяснение:

12/(√7-1)=12(√7+1)/(√7-1)(√7+1)=12/(√7+1)/(7-1)=12(√7+1)/6=2(√7+1).

Answer 2

Ответ:

2√7+2.

Пошаговое объяснение:

Умножим числитель и знаменатель дроби на выражение, сопряжённое выражению √7 -1, то есть, на √7 +1, в знаменателе воспользуемся формулой разности квадратов.

$\displaystyle \frac{12}{ \sqrt{7} - 1} = \frac{12( \sqrt{7} + 1)}{( \sqrt{7} - 1)( \sqrt{7} + 1) } = \frac{12( \sqrt{7} + 1)}{7 - 1} = \frac{12( \sqrt{7} + 1)}{6} = 2( \sqrt{7} + 1) = 2 \sqrt{7} + 2.$

Answer 3

Solving the Expression 12/✓7-1

To solve the given expression 12/✓7-1, we can follow these steps:

1. First, calculate the square root of 7. 2. Then, divide 12 by the result obtained in step 1. 3. Finally, subtract 1 from the result obtained in step 2.

Let's proceed with the calculations.

Calculations

1. Calculate the Square Root of 7: - The square root of 7 is approximately 2.64575131106. - Therefore, the square root of 7 is 2.65 (rounded to two decimal places) [[1]].

2. Divide 12 by the Square Root of 7: - 12 divided by the square root of 7 is approximately 4.52872868507. - Therefore, 12/✓7 is approximately 4.53 (rounded to two decimal places) [[2]].

3. Subtract 1 from the Result: - Subtracting 1 from 4.53 gives us approximately 3.53. - Therefore, the final result of the expression 12/✓7-1 is approximately 3.53 (rounded to two decimal places).

Conclusion

The result of the expression 12/✓7-1 is approximately 3.53.