My problem is:
4 sqrt 81
I know the answer is 3, but I do not know how they got it.
write that as 81^(.25) which is (81^.5)^.5
that is
sqrt ( sqrt 81 )
81 is nine times nine
so
sqrt ( sqrt 81 ) = sqrt (9)
but 9=3*3 so
sqrt (9) = 3
Thank-you, I don't know why I did not think of that. I came up with every other number imaginable but that. I think I was trying toooooooooooooo hard!
5^1/7 in radical notation
(-64)^2/3
To solve the expression 4 sqrt 81, we need to understand what the square root means. The square root of a number is a value that, when multiplied by itself, gives the original number.
In this case, the square root of 81 is a number that, when multiplied by itself, gives 81. So, we need to find a number that satisfies this condition.
One way to find the square root is by using the prime factorization method.
First, let's write 81 as a product of its prime factors:
81 = 3 * 3 * 3 * 3
Now, we group the prime factors into pairs:
81 = (3 * 3) * (3 * 3)
Each pair represents a single factor, so we can simplify:
81 = 9 * 9
Multiplying these two factors together gives us the original number (81).
Now, let's go back to the expression 4 sqrt 81.
The number 4 multiplied by the square root of 81 is equal to the original number (81). We need to find the value of the square root of 81.
From the prime factorization, we know that the square root of 81 is equal to 9.
Therefore, 4 sqrt 81 is equal to 4 * 9, which simplifies to 36.
Therefore, the answer is 36, not 3.
It seems there might be some confusion or misunderstanding. Please verify the question or the intended answer again.