Question

Привет. Ребят, тут тема одна была по алгебре, проходили квадратный корень. Как решать эти примеры: 1.√3m³n³/4a²b 2. √25x²y³/mn7? В последнем примере 7-степень. Нужно именно ход решения обьяснить.

Answer 1

Если понимаешь что такое квадратный корень, то должна понять ход решения.
Для вывода числа из под корня, разбивай число на удобные для тебя степени

Answer 2

How to Solve Square Root Problems with Variables

To solve the given square root problems involving variables, we need to simplify the expressions under the square roots and then evaluate them. Let's go through each example step by step.

Example 1: √(3m³n³)/(4a²b)

To simplify this expression, we can break down the square root into separate square roots for the numerator and denominator:

√(3m³n³) / √(4a²b)

Now, let's simplify each square root separately:

√(3m³n³) = √(3 * m * m * m * n * n * n) = m * n * √(3)

√(4a²b) = 2a * √(b)

Now, we can substitute these simplified square roots back into the original expression:

(m * n * √(3)) / (2a * √(b))

To simplify further, we can cancel out common factors between the numerator and denominator:

(m * n * √(3)) / (2a * √(b)) = (m * n) / (2a) * (√(3) / √(b))

Finally, we can rationalize the denominator by multiplying both the numerator and denominator by √(b):

(m * n * √(3) * √(b)) / (2a * √(b) * √(b)) = (m * n * √(3b)) / (2a * b)

So, the simplified expression is (m * n * √(3b)) / (2a * b).

Example 2: √(25x²y³)/(mn⁷)

Similar to the previous example, let's break down the square root into separate square roots for the numerator and denominator:

√(25x²y³) / √(mn⁷)

Now, let's simplify each square root separately:

√(25x²y³) = 5x * √(y³) = 5x * y^(3/2)

√(mn⁷) = √(m * n * n * n * n * n * n) = n^(7/2) * √(m)

Now, we can substitute these simplified square roots back into the original expression:

(5x * y^(3/2)) / (n^(7/2) * √(m))

To simplify further, we can cancel out common factors between the numerator and denominator:

(5x * y^(3/2)) / (n^(7/2) * √(m)) = (5x * y^(3/2)) / (n^(7/2)) * (1 / √(m))

Finally, we can rationalize the denominator by multiplying both the numerator and denominator by √(m):

(5x * y^(3/2) * √(m)) / (n^(7/2) * √(m) * √(m)) = (5x * y^(3/2) * √(m)) / (n^(7/2) * m)

So, the simplified expression is (5x * y^(3/2) * √(m)) / (n^(7/2) * m).

I hope this explanation helps! Let me know if you have any further questions.