Tell whether each pair of expressions can be simplified to like radicals
√2,√32
To determine whether two expressions can be simplified to like radicals, we need to find the prime factorization of each expression.
Let's start with the expression √2:
The prime factorization of 2 is 2 * 1. Since 2 is a prime number, we cannot simplify √2 any further.
Next, let's look at √32:
The prime factorization of 32 is 2 * 2 * 2 * 2 * 2. We can rewrite √32 as √(2 * 2 * 2 * 2 * 2).
Now, let's compare the prime factorizations of √2 and √32. We have:
√2: 2 * 1
√32: 2 * 2 * 2 * 2 * 2
From the prime factorizations, we can see that the expressions √2 and √32 do not have the same factors. Therefore, they cannot be simplified to like radicals.
In conclusion, the pair of expressions √2 and √32 cannot be simplified to like radicals.