What is the irrational square root √63 rewritten as the product of an integer and another irrational square root, in the simplest form?
To rewrite √63 as the product of an integer and another irrational square root, we can first factor 63 to identify any perfect square factors. The prime factorization of 63 is 3 * 3 * 7. Since 9 is a perfect square factor of 63 (because 9 = 3 * 3), we can rewrite √63 as √(9 * 7).
Using the property of square roots that √(ab) = √a * √b, we can simplify this further:
√(9 * 7) = √9 * √7
Since √9 = 3, the simplified form is:
3√7