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8th Grade Square Roots & Irrational Numbers Worksheets

8th Grade Square Roots & Irrational Numbers: estimate square roots, solve with square and cube roots, and sort rational and irrational numbers. Every worksheet is free, prints as a PDF with an answer key, and can be assigned online. The ones teachers open most are first.

← All 8th grade topics 8.NS.1 8.NS.2 8.EE.2

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8th Grade Square Roots & Irrational Numbers Worksheets - Identifying Rational and Irrational Numbers worksheet

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Identifying Rational and Irrational Numbers

8ns1

Student objectives

Decide whether a number is rational or irrational.
Recognize that fractions, integers, and whole numbers are rational because they can be written as a ratio of integers.
Tell that terminating decimals and repeating decimals are rational numbers.
Identify common irrational numbers like pi and square roots that do not simplify to a fraction.

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8th Grade Square Roots & Irrational Numbers Worksheets - Using Square and Cube Roots worksheet

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Using Square and Cube Roots

8ee2

Student objectives

Find the square root of a perfect square and write the whole-number answer.
Find the cube root of a perfect cube and write the whole-number answer.
Recognize when a number is a perfect square or a perfect cube.

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8th Grade Square Roots & Irrational Numbers Worksheets - Examining Square Root Relative Values worksheet

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Examining Square Root Relative Values

8ns2

Student objectives

Decide which two whole numbers a square root falls between.
Use nearby perfect squares to judge whether a square root is closer to the lower or higher whole number.
Compare the sizes of different square roots by thinking about their values.

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8th Grade Square Roots & Irrational Numbers Worksheets - Examining Square Roots worksheet

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Examining Square Roots

8ns2

Student objectives

Recognize the perfect squares that are closest to a given square root.
Decide which two whole numbers a square root falls between.
Use nearby perfect squares to make a quick estimate of a square root’s size.

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8th Grade Square Roots & Irrational Numbers Worksheets - Examining Powers and Bases worksheet

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Examining Powers and Bases

8ee2

Student objectives

Identify the base and the exponent in an expression written with powers.
Write the full multiplication that a power represents (like 5^3 means 5×5×5).
Evaluate simple powers of integers to find the value.

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8th Grade Square Roots & Irrational Numbers Worksheets - Expressing Decimals with Numberlines worksheet

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Expressing Decimals with Numberlines

8ns2

Student objectives

Practice reading a number line that is divided into equal parts and understanding what each tick mark means.
Learn to locate a decimal on a number line by using the interval between two whole numbers.

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8th Grade Square Roots & Irrational Numbers Worksheets - Perfect Square Roots worksheet

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Perfect Square Roots

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Student objectives

Recognize which numbers are perfect squares (like 36 or 81).
Find the whole-number square root of a perfect square.
Connect squares and square roots (for example, knowing 12×12 matches √144).
Build speed and accuracy with common square root facts.

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8th Grade Square Roots & Irrational Numbers Worksheets - Converting Repeating Decimals to Fractions worksheet

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Converting Repeating Decimals to Fractions

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Student objectives

Recognize when a decimal repeats and identify the repeating part.
Convert a repeating decimal into a fraction using an equation and solving for the value.
Explain why repeating decimals represent rational numbers.

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8th Grade Square Roots & Irrational Numbers Worksheets - Simplifying Radicals worksheet

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Simplifying Radicals

8ns2

Student objectives

Practice rewriting square roots by pulling out perfect-square factors.
Use factor pairs to break a number under a radical into simpler parts.
Simplify radicals all the way to a number times a square root (like 3√2).
Recognize which radicals are already in simplest form.

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8th Grade Square Roots & Irrational Numbers Worksheets - Finding Radicals on a Numberline worksheet

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Finding Radicals on a Numberline

8ns2

Student objectives

Place square roots on a number line by figuring out which two whole numbers they fall between.
Estimate the decimal value of a square root well enough to plot it in the right spot.
Use nearby perfect squares (like 16 and 25) to judge how close a square root is to a whole number.

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8th Grade Square Roots & Irrational Numbers Worksheets - Solving Square Roots worksheet

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Solving Square Roots

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Student objectives

Practice estimating square roots of numbers that aren't perfect squares
Figure out which two whole numbers a square root falls between
Work with square roots of various sizes to build number sense around irrational numbers

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8th Grade Square Roots & Irrational Numbers Worksheets - Solving with Squared and Cubed worksheet

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Solving with Squared and Cubed

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Student objectives

Evaluate expressions with squared and cubed numbers.
Solve simple equations where a number is squared or cubed to find the missing value.
Recognize perfect squares and perfect cubes and match them to their roots.

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8th Grade Square Roots & Irrational Numbers Worksheets - Finding Square and Cube Roots with Equations worksheet

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Finding Square and Cube Roots with Equations

8ns2

Student objectives

Recognize perfect squares and perfect cubes so you can solve quickly without a calculator.

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8th Grade Square Roots & Irrational Numbers Worksheets - Rewriting Factors as Squares worksheet

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Rewriting Factors as Squares

8ns2

Student objectives

Break a number into factors and spot pairs that make a perfect square.
Use exponents to write repeated factors more simply, like 3×3 as 3^2.

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8th Grade Square Roots & Irrational Numbers Worksheets - Solving with Negative Powers worksheet

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Solving with Negative Powers

8ns2

Student objectives

Rewrite negative exponents as reciprocals so the exponent becomes positive.
Evaluate expressions with negative powers to get the correct fraction or decimal value.
Work with negative exponents on whole-number bases, fractions, and powers of 10.

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8th Grade Square Roots & Irrational Numbers Worksheets - Classifying Numbers as Rational or Irrational worksheet

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Classifying Numbers as Rational or Irrational

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Student objectives

Classify numbers as rational or irrational.
Recognize that square roots of non-perfect squares and multiples of pi are irrational.
Recognize that fractions, terminating decimals, integers, and square roots of perfect squares are rational.

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More 8th grade topics

Identifying Functions 9 Transformations 5 Scientific Notation 7 Slope & Rate of Change 8 Comparing & Modeling Linear Functions 11 Laws of Exponents 3 Linear Equations & Systems 2 Pythagorean Theorem 2 Congruent & Similar Figures 5 Angles in Triangles 3 Volume of Cylinders, Cones & Spheres 2

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