what is the square root of 12x^3y^2
square-root of a product is the product of the individual square-roots.
So
√(12x^3y^2 )
=√(4)√(3)√(x²)√(x)√(y²)
=2√(3)x√(x) y
=2xy√(3x)
sqrt(y^2)=absolute value of y ( IyI )
To find the square root of 12x^3y^2, we can break it down into smaller steps.
Step 1: Break down the number inside the square root.
The number inside the square root is 12x^3y^2.
Step 2: Simplify the expression under the square root.
To simplify the expression, we can break down 12 into its prime factors: 12 = 2 * 2 * 3.
Then we can write the expression as:
√(2^2 * 3 * x^3 * y^2)
Step 3: Apply the square root property.
Using the square root property, we can separate the factors inside the square root:
√(2^2) * √(3) * √(x^3) * √(y^2)
Step 4: Simplify each individual square root.
√(2^2) = 2
√(3) = √3
√(x^3) = x^(3/2) (since square root of x^3 is x^(3/2))
√(y^2) = y (since square root of y^2 is y)
Putting it all together, the square root of 12x^3y^2 is:
2xy * √3 * x^(3/2)
To find the square root of a term like 12x^3y^2, we need to break it down into its individual factors and simplify each factor separately.
First, let's identify the factors in 12x^3y^2:
- The number 12 can be broken down into its factors as 2 * 2 * 3.
- The variable x^3 represents x * x * x.
- The variable y^2 represents y * y.
Next, we can simplify each factor:
- The square root of 2 * 2 * 3 is 2√3 since both 2's can be taken outside the square root symbol as a single factor.
- The square root of x * x * x is x^(3/2) since we can take the square root of each x and multiply the exponents.
- The square root of y * y is y since the exponent is already 1.
Combining the simplified factors, the square root of 12x^3y^2 is:
2√(3x^(3/2)y)