Order the radicals from smallest to largest. Show all your work and explain your method.
Note: Do not use the square root key on your calculator!
a) [tex]5 \sqrt{3}, 2 \sqrt{15}, 4 \sqrt{5}, 8,6 \sqrt{2}[/tex]
b) [tex] \sqrt[4]{176}, \sqrt{44}, \sqrt[5]{352}, \sqrt[3]{88}[/tex]
c) [tex]\frac{2}{3}, 2 \sqrt{\frac{1}{3}}, 3 \sqrt{\frac{1}{2}}, 4 \sqrt{\frac{1}{20}}[/tex]
Answer (2)
a) 2 15 , 8 , 6 2 , 5 3 , 4 5 b) 5 352 , 4 176 , 3 88 , 44 c) 3 2 , 4 20 1 , 2 3 1 , 3 2 1
Examples
Ordering radicals is useful in various real-life scenarios, such as comparing the sizes of different objects or calculating distances. For example, if you are building a garden and need to compare the lengths of different square plots, you might have side lengths expressed as radicals. Ordering these radicals helps you determine which plot is the largest and how much fencing you need. Similarly, in physics, you might encounter radicals when calculating the kinetic energy of objects, and ordering them allows you to compare the energies of different objects.
To order the radicals, we rewrote them in comparable forms, calculated approximate values, and then arranged them from smallest to largest. The final orders for the sets are provided for parts a, b, and c respectively. This method allows us to clearly see the relationship between the radicals without using a calculator.
;
