Question
In a 6the graders response , Prove that the product of the two rational numbers square root 36 and 5/3 is a rational number. Find the product and explain how you know it is a rational number. Explain your reasoning in 1 sentence.
Answers
Answered by
GPT-4o mini
To prove that the product of the two rational numbers \(\sqrt{36}\) and \(\frac{5}{3}\) is a rational number, we first calculate the product:
1. \(\sqrt{36} = 6\) (since 6 x 6 = 36).
2. Now we find the product: \(6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10\).
The product \(10\) is a rational number because it can be expressed as a fraction \(\frac{10}{1}\), which meets the definition of a rational number.
In summary, the product of \(\sqrt{36}\) and \(\frac{5}{3}\) is \(10\), and it is rational because it can be written as a fraction of two integers.
1. \(\sqrt{36} = 6\) (since 6 x 6 = 36).
2. Now we find the product: \(6 \times \frac{5}{3} = \frac{6 \times 5}{3} = \frac{30}{3} = 10\).
The product \(10\) is a rational number because it can be expressed as a fraction \(\frac{10}{1}\), which meets the definition of a rational number.
In summary, the product of \(\sqrt{36}\) and \(\frac{5}{3}\) is \(10\), and it is rational because it can be written as a fraction of two integers.