Is this correct
cube root 3√540r^3 s^2 t^9
cube root 3√4(5)(3)(3)(3)r^3s^2 (T^3)^3
3r^t^3 cube root 3√4(5)s^2
3r^t^3 cube root 3√20s^2
is this the answer
3rt cube root 3√20s^2
Without brackets, your question and your answer is ambigious.
I will assume you want
cuberoot(3√540 r^3 s^2 t^9)
= (3√540r^3 r^3 s^2 t^9)^(1/3)
= [3√((36)(15) r^3 s^2 (t^3)^3]^(1/3)
= [ 18√15 r^3 s^2 (t^3)^3]^(1/3)
= (18√15)^(1/3) r s^(2/3) t^3
according to my interpretation of your question
Seems we want cube roots:
∛540r^3 s^2 t^9
= ∛27*20 r^3 s^2 (t^3)^3
= 3rt^3 ∛20s^2
so, yes, you are correct
No, that is not correct. Let's break it down step by step.
The cube root of a number is denoted by the radical symbol (∛), and in this case, we need to find the cube root of 540r^3s^2t^9.
Step 1: Start by simplifying the terms inside the radical separately.
- For 540, you can factor it into 2 * 2 * 3 * 3 * 3 * 5, which can be written as 2^2 * 3^3 * 5.
- For r^3, s^2, and t^9, they remain unchanged inside the radical since they cannot be simplified further.
Step 2: Now, rewrite the expression with the simplified terms.
cube root of 2^2 * 3^3 * 5 * r^3 * s^2 * t^9
Step 3: Let's group the terms in a way that facilitates the simplification.
cube root of (2^2 * r^3 * t^9) * (3^3 * s^2) * 5
Step 4: Take the cube root of each group of terms separately.
cube root of 2^2 * r^3 * t^9 * cube root of 3^3 * s^2 * cube root of 5
Step 5: Simplify each cube root separately.
- cube root of 2^2 * r^3 * t^9 = 2rt^3
- cube root of 3^3 * s^2 = 3s
- cube root of 5 = ∛5
Putting it all together, the simplified expression is: 2rt^3 * 3s * ∛5.