8th Grade Math Worksheets
Eighth grade is where square roots, negative exponents and slope arrive. Students find square and cube roots, estimate the square roots that are not whole numbers, use the rules of exponents, write very large and very small numbers in scientific notation, find the slope of a line, and use the Pythagorean theorem to find a missing side or the distance between two points. Each page below prints a fresh sheet for one skill, with an answer key.
The roots and exponents pages come first because the rest use them: the Pythagorean theorem ends with a square root, and multiplying numbers in scientific notation adds the exponents of the powers of ten. The slope pages read a line’s rise and run from a graph or from two points, and the geometry pages find the hypotenuse, a missing leg, the distance across a coordinate grid, and the third angle of a triangle.
Some of eighth grade has no pages here: turning repeating decimals into fractions, equations with the variable on both sides, systems of two equations, defining and comparing functions, transformations, the volume of cylinders, cones and spheres, and scatter plots and two-way tables.
Roots, exponents and scientific notation
- Square Roots WorksheetsFind the square root of a perfect square.
- Cube Roots WorksheetsFind the cube root of a perfect cube.
- Estimating Square RootsFind the two whole numbers a square root lies between.
- Exponent Rules WorksheetsMultiply and divide powers; zero and negative exponents.
- Scientific Notation WorksheetsWrite numbers in scientific notation and back.
- Multiplying and Dividing in Scientific NotationMultiply and divide numbers in scientific notation.
Lines and slope
Geometry
- Finding the Hypotenuse WorksheetsFind the longest side of a right triangle.
- Pythagorean Theorem WorksheetsHypotenuse, missing leg, and is it a right triangle?
- Distance Between Two Points WorksheetsUse the Pythagorean theorem on a coordinate grid.
- Find the Missing AngleUse the angle sum of a triangle to find the third angle.
Frequently asked questions
What math does 8th grade cover?
Square and cube roots, irrational numbers, the rules of exponents and scientific notation, linear equations and systems of two equations, slope and functions, the Pythagorean theorem, transformations, the volume of cylinders, cones and spheres, and scatter plots. The pages here cover roots and estimating square roots, the rules of exponents, scientific notation, slope from a graph and from two points, the Pythagorean theorem and the distance between two points, and the angles of a triangle.
Why do square roots come before the Pythagorean theorem?
Because the theorem ends with one. A right triangle with legs of 6 and 8 has 6² + 8² = 36 + 64 = 100 for the square of its hypotenuse, so the hypotenuse is √100 = 10. When the sum is not a perfect square, as with legs of 1 and 2, which give √5, the length lies between two whole numbers, here 2 and 3, and estimating square roots is how to find which two.
How does slope build on seventh grade?
Slope is the unit rate of seventh grade’s proportional relationships, read from a line. The line y = 3x rises 3 for every 1 across, so its slope is 3, the same as its constant of proportionality. Eighth grade finds the slope of any line, including lines that go down and lines that miss the origin: from (1, 3) to (4, 9) a line rises 6 while it runs 3, so its slope is 6 ÷ 3 = 2.
Where should a student who finds this hard start?
On the seventh-grade page. Eighth grade leans on signed numbers and on proportional relationships: a slope such as -2/3 is a negative fraction, and the rules of exponents add and subtract negative exponents. The integer pages and the graphing proportional relationships page come before everything here.