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.
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.
Similar Questions
What is the product of square root of, 6, end square root 6 and 2, square root of, 15, end square root2 15 in simplest radical form?
What is the product of 8, square root of, 14, end square root8 14 and 5, square root of, 12, end square root5 12 in simplest radical form?
Express in simplest radical form.start fraction, square root of, 2646, end square root, divided by, square root of, 9, end square root, end fraction9 2646
The product of a real number and its square is 1728. What is the number? 1212√212√38
Express in simplest radical form.square root of, 6, end square root, square root of, 18, end square root6 18
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.