Graduate Management Admission Test (GMAT) Practice Test

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Get ready for the GMAT with challenging questions, detailed hints, and comprehensive explanations. Sharpen your skills and improve your scores. Prepare effectively for your management career goals!

Each practice test/flash card set has 50 randomly selected questions from a bank of over 500. You'll get a new set of questions each time!

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Which of the following equations is true for any numbers a and b?

√(a + b) = (√a) + (√b)
√(a * b) = (√a) x (√b)
√(a/b) = (√a)/(√b)
√(a - b) = (√a) - (√b)

The correct answer is: √(a/b) = (√a)/(√b)

The equation that holds true for any numbers a and b is based on the properties of square roots. The correct equation demonstrates the behavior of square roots with respect to multiplication and division. When considering the property of square roots, it is established that the square root of a product of two numbers is equal to the product of their individual square roots. Therefore, when you have the equation √(a * b), it can be simplified to (√a) * (√b). This holds true as long as a and b are non-negative. For the specific choice that you've selected, the expression √(a/b) = (√a)/(√b) also follows the property of square roots in relation to division. The square root of a fraction can be expressed as the square root of the numerator divided by the square root of the denominator, provided both a and b are non-negative and b is not zero. This property is crucial in algebra and arithmetic as it illustrates how square roots distribute over division. The other options do not maintain their validity universally. The first choice incorrectly suggests that the square root of a sum is equal to the sum of the square roots. The fourth choice implies that the square root of a difference can be simplified to the