Simplify sqrt(72x^3)-5xsqrt(2x). Assume that each radical represents a real number.
I need all of the steps.
Thanks
sqrt(72x^3)-5xsqrt(2x)
=sqrt((6x)²*2x)-5x sqrt(2x)
=6x sqrt(2x)-5x sqrt(2x)
=x sqrt(2x)
To simplify the expression sqrt(72x^3) - 5xsqrt(2x), let's break it down step-by-step:
Step 1: Simplify the square root of 72x^3.
We can rewrite 72x^3 as (36 * 2 * x^2 * x). And since the square root of 36 is 6, we can simplify the square root of 72x^3 as 6x(sqrt(2x)).
Step 2: Rewrite the expression using the simplified term.
Now the expression becomes: 6x(sqrt(2x)) - 5x(sqrt(2x)).
Step 3: Combine like terms.
Combining the terms with sqrt(2x), we get: (6x - 5x)(sqrt(2x)).
Step 4: Simplify the coefficients in front of sqrt(2x).
After combining like terms, we have (6x - 5x)(sqrt(2x)) = x(sqrt(2x)).
Thus, the simplified form of sqrt(72x^3) - 5x(sqrt(2x)) is x(sqrt(2x)).
To simplify the expression √(72x^3) - 5x√(2x), we need to simplify each term individually and then combine them.
Step 1: Simplify the term √(72x^3).
To simplify the square root, we need to find perfect square factors of the number inside the square root. In this case, we have 72x^3.
First, let's break down 72x^3 into its prime factorization:
72 = 2^3 * 3^2
x^3 = x^2 * x
Now, we can rewrite the expression √(72x^3) as √(2^3 * 3^2 * x^2 * x). Since we assume the radical represents a real number, we can simplify the square root by taking out the perfect square factors:
√(2^3 * 3^2 * x^2 * x) = √(2^2 * (2 * 3)^2 * x^2 * x) = 2 * 3 * x * √(2x) = 6x√(2x).
Step 2: Simplify the term -5x√(2x).
This term is already simplified, so there are no further steps needed.
Step 3: Combine the simplified terms.
Combine the terms from Step 1 and Step 2 together:
6x√(2x) - 5x√(2x).
Since both terms have a common factor of x√(2x), we can factor it out:
x√(2x)(6 - 5) = x√(2x)(1) = x√(2x).
Therefore, the simplified form of the expression √(72x^3) - 5x√(2x) is x√(2x).
Note: The assumption that the radical represents a real number means we are assuming that the value inside the square root is non-negative.