Convert each mixed radical to an entire radical and each entire radical to the simplest mixed radical.
1.) ^3 root -192
The answer is -4 exponent 3root 3 but I can't figure out how to get the answer.
2.) -6 exponent 3root 13
The answer is exponent 3 root -2808, but I can't figure out how to get the answer.
∛-192 = ∛(-1*64*3) = -1*4*∛3
-6∛13) = ∛((-6)^3*13) = ∛(-216)(13) = ∛-2808
not sure of your notation.
does ^3 root -192 supposed to mean
the cuberoot of -192 ?
if so , (-192)^(1/3)
= (-64)^(1/3) * (3^(1/3)
= -4 (3)^(1/3) or -4 cuberoot (3)
-6 exponent 3root 13 ??
= (-6)^3 √13 ???
To convert a mixed radical to an entire radical, we need to simplify it by factoring out the perfect cubes under the cube root.
1) ^3√-192:
First, we need to find the largest perfect cube that can be factored out of -192. In this case, the largest perfect cube is 64 (which is 4^3).
We divide -192 by 64:
-192 ÷ 64 = -3
Next, we factor out the perfect cube:
^3√(-3 × 64)
The cube root of 64 is a whole number, 4. So we can simplify further:
4 × ^3√(-3)
Therefore, ^3√-192 can be converted to 4^3√(-3), which can also be written as -4 × ^3√3 (since -3 is the same as -1 × 3).
2) -6^3√13:
To convert an entire radical to the simplest mixed radical, we need to find the largest perfect cube factor of the number under the cube root.
First, find the largest perfect cube that can be factored out of 2808. In this case, the largest perfect cube is 216 (which is 6^3).
Divide 2808 by 216:
2808 ÷ 216 = 13
Now, we have ^3√13 × 6
Therefore, -6^3√13 can be converted to ^3√2808.
So the answer is ^3√2808.