Question

1,5√192 упростить корень​

Answer 1

Ответ:

12√3.

Объяснение:

1,5√192 = 1,5•√(4•16•3) = 1,5•2•4√3 = 12√3.

Answer 2

To simplify the square root of 192, we need to find its prime factorization and then take out the perfect square factors from under the radical sign.

Step 1: Find the prime factorization of 192 192 can be written as: 192 = 2 * 2 * 2 * 2 * 2 * 3

Step 2: Take out perfect square factors from under the radical Among the prime factors, we have four 2's, which form a perfect square: 2 * 2 * 2 * 2 = (2^2) * 2 = 16 So, we can take out 16 from under the radical.

Now, rewrite the square root of 192 with the perfect square factor taken out: √192 = √(16 * 12)

Step 3: Simplify the radical √(16 * 12) = √16 * √12 = 4 * √12

Step 4: Further simplification Now, let's simplify the square root of 12: 12 can be written as 4 * 3, and 4 is a perfect square: 4 * 3 = (2^2) * 3 = 4√3

Step 5: Final answer Putting it all together: √192 = 4 * √12 = 4 * 4√3 = 16√3

So, the simplified form of √192 is 16√3.