Simplify radical expressions.
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Simplifying radicals will be a useful skill for when students compute with radicals in the upcoming lessons. It is helpful for students to be familiar with and to have readily in mind the perfect squares and cubes within 100.
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Determine which value is greater without calculating the value of the radical expression.
a. $${11\sqrt3}$$ _____ $${13\sqrt3}$$
b. $${\sqrt{72}}$$ _____ $${5\sqrt2}$$
c. $${\sqrt{75}}$$ _____ $${2\sqrt{27}}$$
Rewrite each expression as a radical with no perfect squares or cubes remaining inside the radical.
a. $${\sqrt{32x^5y^2}}$$
b. $${2\sqrt[3]{540m^7n^5}}$$
c. $${(24x^2)^{1\over2}}$$
d. $${(24x^2)^{1\over3}}$$
e. $${(24x^2)^{2\over3}}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Simplify each radical so there are no perfect squares or cubes remaining inside the radical.
a. $${\sqrt{54x^8y^5}}$$
b. $${\sqrt[3]{54x^8y^5}}$$