13. is $sqrt{1,815}$ rational? explain.

# Explanation: ## Step1: Recall the definition of rational numbers A rational number can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q\neq0$. A non - perfect - square root is irrational. ## Step2: Check if 1815 is a perfect square We find the prime factorization of 1815. First, divide by 3: $1815\div3 = 605$. Then divide 605 by 5: $605\div5=121$. And $121 = 11\times11$. So, $1815=3\times5\times11^{2}$. Since 1815 is not a perfect square (the exponents of 3 and 5 are 1), $\sqrt{1815}$ cannot be written as a fraction of two integers. # Answer: No, $\sqrt{1815}$ is not rational because 1815 is not a perfect square.