All solutions for 216−−−√3
would be
The solutions for √3 can be obtained by taking both the positive and negative square root of 3. Thus, the solutions for 216−−−√3 are:
√3 = 1.732
-√3 = -1.732
To find all solutions for the expression √216 - 3, we can follow these steps:
Step 1: Simplify the expression inside the square root.
216 can be factorized as 6^3, so √216 can be written as √(6^3).
Step 2: Apply the properties of radicals.
√(6^3) can be written as (6^3)^(1/2).
By applying the property (a^m)^n = a^(m*n), we can simplify it to 6^(3/2).
Step 3: Evaluate the expression.
6^(3/2) represents the square root of 6 raised to the power of 3/2.
To find all solutions, we need to consider both the positive and negative square roots.
Positive solution:
6^(3/2) = √(6^3) = √(36) = 6
Negative solution:
-6^(3/2) = -√(6^3) = -√(36) = -6
Therefore, the two solutions for the expression √216 - 3 are 6 and -6.
wrong
To find all solutions for the equation 216 - √3, we need to first clarify what type of solutions we are looking for. If we are looking for real solutions, we can solve it algebraically by setting the equation equal to zero and finding the value of the variable.
Let's call the variable x. Our equation is then:
x = 216 - √3
To isolate the square root, we subtract 216 from both sides:
x - 216 = -√3
Next, we square both sides to eliminate the square root:
(x - 216)^2 = (-√3)^2
x^2 - 432x + 46656 = 3
Now, we have a quadratic equation. We can rearrange it and solve it using the quadratic formula or factoring.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation x^2 - 432x + 46656 = 3, a = 1, b = -432, and c = 46653.
Calculating the discriminant (b^2 - 4ac):
D = (-432)^2 - 4(1)(46653) = 186624 - 186612 = 12
Since the discriminant is positive, we have two real solutions. Plugging the values into the quadratic formula:
x = (-(-432) ± √(12)) / (2(1))
x = (432 ± √12) / 2
Simplifying:
x1 = (432 + √12) / 2
x2 = (432 - √12) / 2
So, the two real solutions for the equation 216 - √3 are (432 + √12) / 2 and (432 - √12) / 2.
If you are looking for complex solutions, you can use the same algebraic approach and solve for the variable. However, in this case, you would end up with complex numbers as solutions.
Apologies for the mistake. Let's go through the steps again to find the correct solutions for the expression √216 - 3.
Step 1: Simplify the expression inside the square root.
√216 can be simplified by finding the largest perfect square that divides 216. The largest perfect square that divides 216 is 36 (6^2), so we can write √216 as √(6^2 * 6).
Step 2: Apply the properties of radicals.
Using the property √(ab) = √a * √b, we can rewrite √(6^2 * 6) as (√6 * √6) * √6. This simplifies to 6√6.
Step 3: Evaluate the expression.
Now we can substitute 6√6 back into the original expression: 6√6 - 3.
Therefore, the solution for the expression √216 - 3 is 6√6 - 3.
My square table has an area of 36 square feet. What is the side length of my table?(1 point)
feet
To find the side length of the square table with an area of 36 square feet, you can use the formula for the area of a square, which is side length squared.
Let's denote the side length of the table as x. The formula for the area of a square is A = x^2, where A represents the area.
Given that the area of the table is 36 square feet, we can set up the equation as follows:
x^2 = 36
To solve for x, we can take the square root of both sides of the equation:
√(x^2) = √36
Simplifying,
x = ±√36
The square root of 36 is 6, so the possible side lengths for the table are +6 and -6. However, in the context of a physical table, we consider only positive values for length.
Therefore, the side length of your square table is 6 feet.
A shipping box in the shape of a cube has a volume of 512 cubic inches. What is the edge length of this box?
To find the edge length of the cube-shaped shipping box with a volume of 512 cubic inches, we can solve for the side length using the formula for the volume of a cube.
The formula for the volume of a cube is given by V = s^3, where V represents the volume and s represents the side length.
Given that the volume of the box is 512 cubic inches, we can set up the equation as follows:
s^3 = 512
To solve for s, we can take the cube root of both sides of the equation:
∛(s^3) = ∛512
Simplifying,
s = ∛512
Calculating the cube root of 512, we find that s is equal to 8.
Therefore, the edge length of the shipping box is 8 inches.