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Questions and Answers
What is the value of $x$ in the equation $x^2 - 8 = 28$?
What is the value of $x$ in the equation $x^2 - 8 = 28$?
- 4
- 6 (correct)
- 36
- 196
If $x^2 + 14 = 95$, what is the value of $x$?
If $x^2 + 14 = 95$, what is the value of $x$?
- 11
- 7
- 9 (correct)
- 81
Solve for $x$ in the equation $\frac{1}{2}x^3 - 11 = 21$.
Solve for $x$ in the equation $\frac{1}{2}x^3 - 11 = 21$.
- 8
- 2
- 64
- 4 (correct)
What is the value of $x$ that satisfies the equation $2x^3 - 7 = -61$?
What is the value of $x$ that satisfies the equation $2x^3 - 7 = -61$?
A cube has a volume of 27 cm³. What is the length of one side of the cube?
A cube has a volume of 27 cm³. What is the length of one side of the cube?
A cube has a volume of 27 cm³. What is the surface area of the cube?
A cube has a volume of 27 cm³. What is the surface area of the cube?
If $x^2 = 169$, what are the possible values of $x$?
If $x^2 = 169$, what are the possible values of $x$?
Determine the value of $x$ in the equation: $x^3 + 5 = 32$.
Determine the value of $x$ in the equation: $x^3 + 5 = 32$.
Solve for $x$: $\frac{x^2}{4} = 9$.
Solve for $x$: $\frac{x^2}{4} = 9$.
If the area of a square is 64 cm², what is the length of one side?
If the area of a square is 64 cm², what is the length of one side?
What is the solution to the equation $\sqrt{x} = 7$?
What is the solution to the equation $\sqrt{x} = 7$?
Determine the value of $x$ that satisfies $5x^2 = 45$.
Determine the value of $x$ that satisfies $5x^2 = 45$.
If a cube's side length is 5 cm, what is its volume?
If a cube's side length is 5 cm, what is its volume?
Find the value of $x$ in the equation $x^2 - 1 = 24$.
Find the value of $x$ in the equation $x^2 - 1 = 24$.
What is the side length of a square with an area of 144 cm²?
What is the side length of a square with an area of 144 cm²?
Solve for $x$: $x^3 = -8$.
Solve for $x$: $x^3 = -8$.
What is the value of $x$ in the equation $3x^2 = 75$?
What is the value of $x$ in the equation $3x^2 = 75$?
If the volume of a cube is 64 cm³, what is the area of one face of the cube?
If the volume of a cube is 64 cm³, what is the area of one face of the cube?
A square has a perimeter of 32 cm. What is the length of each side?
A square has a perimeter of 32 cm. What is the length of each side?
Flashcards
Solving x² - 8 = 28
Solving x² - 8 = 28
To find x, add 8 to both sides, then take the square root.
Solving x² + 14 = 95
Solving x² + 14 = 95
To find x, subtract 14 from both sides, then take the square root.
Solving 0.5x³ - 11 = 21
Solving 0.5x³ - 11 = 21
To find x, add 11 to both sides of the equation and multiply by two-thirds, then take the cube root.
Solving 2x³ - 7 = -61
Solving 2x³ - 7 = -61
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Surface area of cube with volume 27cm³
Surface area of cube with volume 27cm³
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Study Notes
- These notes are for a square and cubic roots pre-assessment, and a calculator is not permitted.
Solving Equations for x
- To solve (x^2 - 8 = 28), add 8 to both sides to get (x^2 = 36), then take the square root to find (x = 6).
- To solve (x^2 + 14 = 95), subtract 14 from both sides to get (x^2 = 81), then take the square root to find (x = 9).
- To solve (\frac{1}{2}x^3 - 11 = 21), add 11 to both sides to get (\frac{1}{2}x^3 = 32), multiply both sides by 2 to get (x^3 = 64), then take the cubic root to find (x = 4).
- To solve (2x^3 - 7 = -61), add 7 to both sides to get (2x^3 = -54), divide both sides by 2 to get (x^3 = -27), then take the cubic root to find (x = -3).
Cube Volume and Surface Area
- Given a cube with a volume of 27cm³, the side length (x) can be found by taking the cubic root of 27, resulting in (x = 3) cm.
- The surface area ((SA)) of a cube is calculated by (6 \cdot x^2).
- For a cube with side length 3 cm, the surface area is (6 \cdot 3^2 = 6 \cdot 9 = 54) cm².
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