3 radical 4x^2 time s radical 6x^4 times 3radical 9x
If you mean
3 sqrt(4x^2)*sqrt(6x^4)*3sqrt(9x),
thet equals
3*2x*sqrt6*x^2*9*sqrtx
= 54 sqrt6*x^(7/2)
I could not figure out what was intended.
To simplify the expression 3√(4x^2) * √(6x^4) * 3√(9x), you can follow these steps:
Step 1: Simplify the individual radicals
- For the first term, 3√(4x^2), you can simplify the square root by taking out the square root of 4 (which is 2) from underneath the radical sign. This leaves us with 2x.
- For the second term, √(6x^4), there are no perfect square factors in the radicand, so we cannot simplify it further.
- For the third term, 3√(9x), you can simplify the cube root by taking out the cube root of 9 (which is 3) from underneath the radical sign. This leaves us with 3x.
Step 2: Multiply the simplified terms
After simplifying the individual radicals, you multiply the simplified terms together:
2x * √(6x^4) * 3x
Step 3: Simplify the square root of 6x^4
To simplify the square root of 6x^4, we can break it down as follows:
2x * √(6x^2 * x^2)
We can take the square root of x^2, which leaves us with just x under the radical sign:
2x * √(6x^2) * x
Step 4: Simplify the square root of 6x^2
To simplify the square root of 6x^2, we can break it down as follows:
2x * √(6) * √(x^2) * x
The square root of x^2 is x, so we can simplify it further:
2x * √(6) * x^2
Step 5: Multiply the simplified terms
Now we can multiply the simplified terms together:
2x * √(6) * x^2 = 2x * x^2 * √(6)
Step 6: Simplify the expression
To simplify the expression, we can simplify the powers of x by adding the exponents:
2x * x^2 = 2x^3
Therefore, the simplified expression is 2x^3 * √(6).