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Can the fraction under the square root be reversed when dividing? For example, 2/3 : √1/2 = 2/3 * √2/1

When dividing a fraction by a square root, it is not possible to simply reverse the fraction under the square root. The process of dividing fractions involves multiplying the numerator by the reciprocal of the denominator. However, when dealing with square roots, the reciprocal of the fraction under the square root cannot be taken directly.

To divide a fraction by a square root, we need to rationalize the denominator. This means eliminating the square root from the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of a binomial is obtained by changing the sign between the terms.

Let's take the example mentioned: 2/3 : √1/2

To divide this fraction, we need to rationalize the denominator:

  1. Multiply the numerator and denominator by the conjugate of the denominator: (2/3) (√2/1) (√2/√2)
  2. Simplify the expression: (2/3) * (√4/√2)
  3. Further simplify by taking the square root of 4: (2/3) * (2/√2)
  4. Multiply the numerators and denominators: (4/3√2)

Therefore, the result of dividing 2/3 by √1/2 is 4/3√2.

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