Multiply and divide rational exponent expressions and radical expressions.
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All of the following equations are true.
$${\sqrt{16}\cdot\sqrt9=\sqrt{144}}$$ $${{\sqrt{80}\over\sqrt{4}}=\sqrt{20}}$$ $${\sqrt5\cdot\sqrt[3]{5}=\sqrt[6]{5^5}}$$
a. What general rules can you determine from these examples?
b. Find the products or quotients below
i. $${\sqrt{12}\cdot\sqrt2}$$
ii. $${\sqrt[3]{4}\cdot\sqrt[3]{3}\cdot\sqrt[3]{5}}$$
iii. $${\sqrt2\cdot\sqrt3\cdot\sqrt[3]{6}}$$
iv. $${\sqrt[3]{45}\over\sqrt[3]{5}}$$
Multiply and simplify as much as possible.
a. $${-5\sqrt{12}\cdot\sqrt8}$$
b. $${\sqrt[3]{6x^2}\cdot\sqrt[3]{9x^4}}$$
Divide and simplify as much as possible.
c. $${2\sqrt{6}\div\sqrt{24}}$$
d. $${\sqrt{120m^9}\over{10\sqrt{4m^4}}}$$
Compute and simplify.
a. $${\sqrt{10}\cdot2\sqrt[3]{10}}$$
b. $${3\sqrt[3]{16}\div2\sqrt[3]{54}}$$
This Anchor Problem is optional and can be moved to the problem set depending on the timing of your class and/or needs of your students.
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The following resources include problems and activities aligned to the objective of the lesson. They can be used to create a problem set for class (for non-Fishtank Plus users), or as supplementary or additional resources to the pre-made Problem Set (for Fishtank Plus users).
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Find the error in each solution. Then find the correct product or quotient.
a. $${\sqrt{20}\cdot\sqrt[3]{5}=\sqrt{100}=10}$$
b. $${{{4\sqrt{35}}\over{\sqrt{28}}}={{4\sqrt{5\cdot7}}\over{\sqrt{4\cdot7}}}={\sqrt5}}$$