What is the irrational square root √63 rewritten as the product of an integer and another irrational square root, in simplest form
To rewrite √63 as the product of an integer and another irrational square root, we need to find a perfect square that is a factor of 63.
Taking a closer look at the prime factorization of 63:
63 = 3 × 3 × 7
We can see that 63 has a perfect square factor of 9 (which is 3 × 3).
Now, let's rewrite 63 as the product of 9 and another factor:
√63 = √(9 × 7)
Using the property of square roots, we can separate the two factors and write it as:
√63 = √9 × √7
Simplifying, we have:
√63 = 3√7
So, the irrational square root √63 can be rewritten as the product of an integer (3) and another irrational square root (√7) in simplest form.
To rewrite √63 as the product of an integer and another irrational square root, we need to find a perfect square factor of 63. The largest perfect square that goes into 63 is 9, which is equal to 3^2.
So, we can rewrite √63 as √(9 * 7). Breaking it down further, we have:
√(9 * 7) = √9 * √7
Now, √9 is an integer and it is equal to 3. Therefore, we can rewrite √63 as:
√63 = 3√7
Hence, the irrational square root √63 can be rewritten as the product 3√7, where 3 is an integer and √7 is another irrational square root.
To rewrite the irrational square root √63 as the product of an integer and another irrational square root in simplest form, let's break down this process step by step:
Step 1: Find the prime factorization of 63.
Start by finding the prime factors of 63: 3 and 7. Since there is no perfect square within these factors, we can simplify √63 further.
Step 2: Simplify the square root.
Rewrite √63 as √(9 * 7). Since 9 is a perfect square (3 * 3 = 9), we can simplify this expression as √9 * √7.
Step 3: Rewrite the integer and irrational square root.
√9 is equal to 3, so we can rewrite the expression as 3√7.
Therefore, the irrational square root √63 can be rewritten as the product of an integer and another irrational square root in simplest form as 3√7.