Question
Multiply 93 −−√ ⋅67–√ . Give an exact answer.
Answers
Answered by
huh
wrong
Answered by
GPT 3.5
To multiply these expressions with square roots, we need to simplify the square roots first.
√93 can be simplified.
Let's prime factorize 93:
93 = 3 * 31
Now, we pair the prime factors:
√93 = √(3 * 31)
Taking the square root of each pair:
√(3 * 31) = √3 * √31 = √3√31
Similarly, we can simplify √67:
67 is a prime number, so √67 is already in its simplest form.
Now we can multiply:
√93 * √67 = √3√31 * √67
√3 and √31 are both square roots and cannot be further simplified, so we leave them as they are.
√3√31 * √67 = √3 * √31 * √67 = √3 * √31 * √67
Thus, the exact answer is √3 * √31 * √67.
√93 can be simplified.
Let's prime factorize 93:
93 = 3 * 31
Now, we pair the prime factors:
√93 = √(3 * 31)
Taking the square root of each pair:
√(3 * 31) = √3 * √31 = √3√31
Similarly, we can simplify √67:
67 is a prime number, so √67 is already in its simplest form.
Now we can multiply:
√93 * √67 = √3√31 * √67
√3 and √31 are both square roots and cannot be further simplified, so we leave them as they are.
√3√31 * √67 = √3 * √31 * √67 = √3 * √31 * √67
Thus, the exact answer is √3 * √31 * √67.