Solve x Cubed Equals p, One Solution

Teach x² = p and x³ = p side by side so students see why one has two solutions and the other has one. Assign the isolate first sheets next, then use the maze and path puzzle for review.

Solve x³ = p for its one solution, with values such as negative 1,000, 27/64 and 0.064. Every number has exactly one cube root, and it has the same sign as the number, so x³ = p has one solution. The directions on the page read: Solve each equation by taking the cube root of both sides. Write the solution on the line. Write fraction answers as fractions. An answer key is included.

Yes, both. We made it for 8th grade square and cube roots, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Every positive number has two square roots, one positive and one negative, and both give the same number when squared. So x² = 64 has the solutions 8 and negative 8, written x = ±8.

Every number has exactly one cube root, with the same sign as the number. So x³ = negative 8 has the single solution x = negative 2.

Get x² alone first with inverse operations. Subtract 5 to get 3x² = 48, divide by 3 to get x² = 16, then take the square root to get x = ±4. Square Root Equations, Isolate x Squared First has 10 equations like this.