Approximating Irrational Numbers

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Avatar for Kate BauerKate Bauer, BP BY-NC
Subject: Math
Grade: 8
Standards: 8.NS.A.28.NS.A.1

This Grade 8 assignment contains 10 questions where students focus on irrational numbers and their approximations. These exercises provide practice for The Number System.

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10 questions

Approximating Irrational Numbers

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Write exact answers in radical form. Round approximations to the nearest hundredth.

1) A square garden has area 34 square feet. What is the exact length of each side of the garden?

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2) What is the approximate length of each side of the garden?

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3) A square piece of carpeting has area 85 square feet. What is the exact length of each side of the piece of carpeting?

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4) What is the approximate length of each side of the piece of carpeting?

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Write exact answers in terms of π\pi. Round approximations to the nearest hundredth.

5) A circle has a diameter of 10 inches. What is the exact circumference of the circle?

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6) What is the approximate circumference of the circle?

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7) A memorial is in the shape of a semicircle with a diameter of 24 feet. What is the exact length of the semicircle?

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8) What is the approximate length of the semicircle?

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9) A spherical bar of soap has a radius of 3 centimeters. What is the exact volume of the bar of soap?

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10) What is the approximate volume of the bar of soap?

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