third root -72 simplified
The third root of -72 simplified is:
-2
wronng
Apologies for the mistake. Let's correct it.
The third root of -72 simplified is:
-2√2
wrong
I apologize for the confusion. Let's try again.
The third root of -72 simplified is a complex number, since it involves taking the cube root of a negative number. The simplified form is:
∛(-72) = -2∛(9) = -2∛(3²) = -2(3∛3) = -2∛3
So, the correct simplified form is:
-2∛3
To simplify the third root of -72, you need to find the prime factors of -72.
The prime factorization of -72 is:
-72 = -1 * 2 * 2 * 2 * 3 * 3
Now, group the factors into triples and rewrite each triple as a single term:
-72 = -1 * (2*2*2) * (3*3) = -1 * 8 * 9 = -72
Therefore, the simplified third root of -72 is -2 * √9, which is equal to -2 * 3 = -6.
To simplify the third root of -72, we need to find the value that, when multiplied by itself three times, equals -72.
First, let's prime factorize -72:
-72 = -1 * 2 * 2 * 2 * 3 * 3 = -1 * 2^3 * 3^2
Now, we need to group the factors in sets of three, since we want to find the third root:
(-1 * 2^3 * 3^2) = (-1 * 2 * 2 * 2) * (3 * 3) = -1 * 2^3 * 3^2
We can see that (-1 * 2^3 * 3^2) can be rearranged as (-1 * 2 * 2 * 2) * (3 * 3). Taking the third root of each group, we get:
(-1 * 2 * 2 * 2) * (3 * 3) = (-1 * 2^1 * 3^1) * (2^1 * 3^1)
Now, we can simplify further by taking out the multiplication with the same base:
(-1 * 2^1 * 3^1) * (2^1 * 3^1) = -1 * 2^1 * 2^1 * 3^1 * 3^1
Next, we simplify the exponents by adding them:
-1 * 2^1 * 2^1 * 3^1 * 3^1 = -1 * 2^(1+1) * 3^(1+1) = -1 * 2^2 * 3^2
Finally, we have simplified the third root of -72:
∛-72 = -1 * 2^2 * 3^2 = -12