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
All solutions for 216−−−√3
would be
7 answers
wrong
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.
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
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.
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.
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.
1 answer