Multiply (5sqrt(19)) / (6sqrt(2)) Give an exact answer

Answer 1

To multiply (5√19) / (6√2), we can simplify the expression using the property √(a) / √(b) = √(a/b):

(5√19) / (6√2) = (5/6) * (√19 / √2)

Next, we can rationalize the denominator by multiplying both the numerator and denominator by √2:

(5/6) * (√19 / √2) = (5/6) * (√19 / √2) * (√2 / √2)

Simplifying the expression further:

(5/6) * (√19 / √2) * (√2 / √2) = (5/6) * (√19 * √2) / (√2 * √2)

Multiplying the square roots:

(5/6) * (√19 * √2) / (√2 * √2) = (5/6) * √(19*2) / √(2*2)

Simplifying the square roots:

(5/6) * √(19*2) / √(2*2) = (5/6) * √38 / 2

Finally, simplifying the fraction:

(5/6) * √38 / 2 = (5√38) / (6*2)

Simplifying further:

(5√38) / (6*2) = (5√38) / 12

Therefore, the exact answer is (5√38) / 12.