Radical and Rational Exponent
find roots
square roots of 12a^3/25=6a^3
-3-square roots 18/-6=-1 this is my answer am I right.
check this for me it find the roots of the problem
I am unable to determine what the problem is.
Is it this?
Sqrt((12a^3)/25)=6a^3 ?
divide by 6a^3
sqrt (12a^3/(36a^6 *25)=1
SQUARE BOTH SIDES
1/(3a^3*25)=1
a^3=1/125
a= 1/5
Radical and Rational Exponent
find roots
square roots of 12a^3/25
check this for me it find the roots of the problem
To find the roots of the equation, let's break down the problem step by step:
1. Start with the given equation: square root of (12a^3/25) = 6a^3
2. Square both sides of the equation to eliminate the square root: (square root of (12a^3/25))^2 = (6a^3)^2
3. Simplify both sides: 12a^3/25 = 36a^6
4. Multiply both sides by 25 to eliminate the fraction: (25 * 12a^3)/25 = 36a^6 * 25
This simplifies to: 12a^3 = 900a^6
5. To make it easier to solve, divide both sides by 12a^3: 12a^3/12a^3 = 900a^6/12a^3
This simplifies to: 1 = 75a^3
6. Divide both sides by 75 to isolate a^3: (1 / 75) = (75a^3) / 75
This simplifies to: 1/75 = a^3
7. Take the cube root of both sides to solve for 'a': (1/75)^(1/3) = (a^3)^(1/3)
This simplifies to: 1/∛75 = a
8. The cube root of 75 is ∛75, so the final answer is:
a = 1/∛75
Now, let's simplify the expression 1/∛75:
1. ∛75 can be rewritten as 75^(1/3)
2. To rationalize the denominator, multiply both numerator and denominator by (∛75)^2:
(1 * (∛75)^2) / (∛75 * (∛75)^2)
Simplifying, we get: (∛75^2) / 75
3. ∛75^2 simply equals 75^(2/3), so the final answer is:
a = 75^(2/3) / 75
Thus, the roots of the equation are a = 75^(2/3) / 75. It seems that your answer of -1 is incorrect.