Divide 2√65/√5. Provide an exact answer.

Answer 1

To divide 2√65 by √5, we need to rationalize the denominator (get rid of the square root).

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of √5 is -√5.

So, multiplying the numerator and denominator by -√5, we get:

2√65 * -√5 = -2√(65*5) = -2√(325) = -2√(5*65) = -2√(5)√(65) = -2√5√65

And √5 * -√5 = -5

Therefore, we have:

(-2√5√65) / -5

Simplifying, we divide both terms by -1:

2√5√65 / 5

Combining the square roots, we get:

2√(5*65) / 5

Which simplifies to:

2√(325) / 5

So, the exact answer is 2√(325) / 5.