yes, i typed it wrong
it should be:
simplify:
√͞ 12x^20 y^8
is the answer
2 √͞ 3x^10y^4
i ask bec i checked a radical calculator but it said
2y^4 x^10 √͞ 3
can you explain the steps if I am wrong
thank you
type it this way:
√(12x^20 y^8)
= √12 √(x^20) √(y^8)
= 2√3 x^10 y^4
sqrt(12x^20y^8) = sqrt(3*4x^20y^8) = sqrt(3)*2x^10 y^4.
To simplify √(12x^20y^8), let's break it down step by step:
Step 1: Prime-factorize the number inside the square root.
12 can be prime-factorized as 2 * 2 * 3.
So, we have: √(2^2 * 3 * x^20 * y^8)
Step 2: Rewrite the variables with even exponents outside of the square root.
In this case, we have x^20 and y^8.
Since x^20 is an even exponent, we can express it as (x^10)^2.
Similarly, y^8 can be expressed as (y^4)^2.
Now, our expression is: √(2^2 * 3 * (x^10)^2 * (y^4)^2 * y^4)
Step 3: Simplify the square root.
Take out the perfect squares from underneath the square root.
We have 2^2, (x^10)^2, and (y^4)^2.
This simplifies the expression to: 2x^10y^4√(3 * y^4)
Step 4: Arrange the terms.
The convention is to write the numeric coefficient first, followed by the variables, and then the square root term.
Therefore, the simplified answer is: 2√(3) * x^10 * y^4
So, the expression you initially provided (2√(3) * x^10 * y^4) is correct. The radical calculator must have provided a different order for the terms, which does not affect the correctness of the simplified expression.