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Find the product of square root of, 23, end square root 23​ and 2, square root of, 23, end square root2 23​ in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

Question

Find the product of square root of, 23, end square root 23​ and 2, square root of, 23, end square root2 23​ in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

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Solution

The product of √23 and 2√23 can be calculated as follows:

Step 1: Write down the multiplication of the two expressions. √23 * 2√23

Step 2: Multiply the numbers outside the square root and the numbers inside the square root separately. = 2 * (√23 * √23)

Step 3: Simplify the multiplication inside the square root. = 2 * 23

Step 4: Multiply the numbers. = 46

So, the product of √23 and 2√23 is 46.

The result is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers and the denominator is not zero. In this case, 46 can be expressed as 46/1. A number is irrational if it cannot be expressed as a fraction of two integers.

This problem has been solved

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