Multiply 93 −−√ ⋅67–√ . Give an exact answer

Answer 1

To multiply the expressions, we need to multiply the square roots as well as the numbers outside the square roots.

Starting with the numbers outside the square roots:
93 * 67 = 6219

Now, let's multiply the square roots:
√93 * √67 = √(93 * 67)

To multiply 93 and 67 inside the square roots, we first prime factorize each number:
93 = 3 * 31
67 = 67

Multiplying the prime factors:
93 * 67 = (3 * 31) * 67 = 3 * 31 * 67

Now, let's simplify the square root:
√(93 * 67) = √(3 * 31 * 67)

Since there are no square factors left, we can't simplify further.

Putting it all together:
93 −−√ ⋅67–√ = √(93 * 67) = √(3 * 31 * 67) = (√3)(√31)(√67) = (√3)(√31)(√67)

So the exact answer is (√3)(√31)(√67).

Answer 2

Divide 265√5√ . Provide an exact answer.

Answer 3

To divide the expression, we need to divide both the numbers outside the square root and the square root terms.

Starting with the numbers outside the square roots:
265 ÷ 5 = 53

Now, let's divide the square roots:
√(265) ÷ √(5)

To divide the square roots, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator (which is √5):
(√(265) ÷ √(5)) * (√(5) ÷ √(5)) = (√(265) * √(5)) ÷ (√(5) * √(5))

Simplifying the denominator:
(√(265) * √(5)) ÷ (√(5) * √(5)) = (√(265) * √(5)) ÷ 5

Now, let's simplify the square roots:
√(265) * √(5) = √(265 * 5) = √(1325)

So, the final expression is:
(√(265) * √(5)) ÷ 5 = √(1325) ÷ 5

The exact answer is √(1325) ÷ 5.