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CCSS 8.NS.2 Worksheets

CCSS 8.NS.2 (Common Core, 8th Grade): "Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π² ).
For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. ." The worksheets below practice this standard. Each one is a free printable PDF with an answer key, comes in multiple versions, and can also be assigned digitally - no login or account needed.

The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. 2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π² ).
For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

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CCSS 8.NS.2 Worksheets - Examining Square Root Relative Values worksheet

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Examining Square Root Relative Values

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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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CCSS 8.NS.2 Worksheets - Examining Square Roots worksheet

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Examining Square Roots

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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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CCSS 8.NS.2 Worksheets - Finding Radicals on a Numberline worksheet

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Finding Radicals on a Numberline

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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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CCSS 8.NS.2 Worksheets - Finding Square and Cube Roots with Equations worksheet

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Finding Square and Cube Roots with Equations

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

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CCSS 8.NS.2 Worksheets - Rewriting Factors as Squares worksheet

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Rewriting Factors as Squares

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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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CCSS 8.NS.2 Worksheets - Simplifying Radicals worksheet

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Simplifying Radicals

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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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CCSS 8.NS.2 Worksheets - Solving Square Roots worksheet

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Solving Square Roots

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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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CCSS 8.NS.2 Worksheets - Solving with Negative Powers worksheet

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Solving with Negative Powers

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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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CCSS 8.NS.2 Worksheets - Expressing Decimals with Numberlines worksheet

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Expressing Decimals with Numberlines

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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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