11√19 - 5√19
whats the difference?
The difference between 11√19 and 5√19 is 6√19.
multiply (5√19) (6√2) give an exact answer
To multiply (5√19) and (6√2), we can apply the distributive property.
(5√19) (6√2) = 5*6*(√19*√2) = 30√(19*2) = 30√38
Therefore, the exact answer is 30√38.
simplify √48
To simplify √48, we need to find the largest perfect square that is a factor of 48. We can see that 16 is the largest perfect square that divides 48.
√48 = √(16 * 3)
Since the square root can be distributed over multiplication, we can simplify further:
√(16 * 3) = √16 * √3 = 4√3
Therefore, √48 simplifies to 4√3.
simplify 3^√54
To simplify 3^√54, we can rewrite 54 as a product of perfect square factors:
54 = 9 * 6 = 3^2 * 2 * 3
Now we can rewrite 3^√54 using exponent rules:
3^√54 = 3^(√(3^2 * 2 * 3))
Since the square root (denoted by √) and the exponent of 2 are inverse operations, we can simplify further:
3^(√(3^2 * 2 * 3)) = 3^(√(3^2) * √(2) * √(3))
Since √(3^2) is simply 3 and √(2) and √(3) cannot be simplified further, we have:
3^(√(3^2) * √(2) * √(3)) = 3^(3 * √(2) * √(3))
Therefore, the simplified form of 3^√54 is 3^(3 * √(2) * √(3)).