Multiply (5sqrt(19)) / (6sqrt(2)) Give an exact answer
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.
To multiply the given expression, you need to follow these steps:
Step 1: Simplify the expression by multiplying the coefficients and then multiplying the square roots.
Given expression: (5√19) / (6√2)
The coefficient of the first term is 5, and the coefficient of the second term is 6.
So, multiplying the coefficients gives us 5 * 6 = 30.
The square root of 19 cannot be simplified further, so it remains as √19.
Similarly, the square root of 2 cannot be simplified further, so it remains as √2.
Now, the expression becomes (30√19) / (6√2).
Step 2: Simplify further by canceling out common factors.
In this case, we can cancel out the common factor of 6 between the numerator and denominator.
So, (30√19) / (6√2) simplifies to (5√19) / √2.
Step 3: Rationalize the denominator to get the exact answer.
To rationalize the denominator, we need to multiply both the numerator and denominator by the square root of 2 (√2).
(5√19) / √2 * (√2 / √2)
Multiplying the numerator and denominator, we get:
(5√19 * √2) / (√2 * √2)
Simplifying further, we have:
(5√38) / 2
Therefore, the exact answer is (5√38) / 2.
To multiply (5√19) / (6√2) and obtain an exact answer, we can proceed with the following steps:
Step 1: Simplify the expression by multiplying the numerators and denominators separately.
(5√19) / (6√2) = (5/6) * (√19/√2)
Step 2: Rationalize the denominator by multiplying it by its conjugate (√2).
(5/6) * (√19/√2) = (5/6) * (√19/√2) * (√2/√2)
Step 3: Simplify the expression in the numerator and denominator.
(5 * √19 * √2) / (6 * √2 * √2) = (5√38) / (6 * 2)
Step 4: Continue simplifying.
(5√38) / (6 * 2) = (5 * √38) / 12
Therefore, the exact answer for (5√19) / (6√2) is (5√38) / 12.