# Approximating Irrational Numbers

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

10 questions

# Approximating Irrational Numbers

**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?

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

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

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

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

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

6) What is the approximate circumference of the circle?

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

8) What is the approximate length of the semicircle?

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

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