Documenting Procedures for Radical Expressions

Standard Operating Procedure: Combining Radical Expressions

Simplifying $8\sqrt{2} - 9\sqrt{2}$, $4\sqrt[3]{x} + 7\sqrt[3]{x}$, and $3\sqrt[4]{x} - 5\sqrt[4]{y}$

Simplifying $5\sqrt{3} - 9\sqrt{3}$, $5\sqrt[3]{y} + 3\sqrt[3]{y}$, and $5\sqrt[4]{m} - 2\sqrt[3]{m}$

Simplifying $2\sqrt{2} - 7\sqrt{2}$

Simplifying $2\sqrt{5n} - 6\sqrt{5n} + 4\sqrt{5n}$

Simplifying $\sqrt[4]{3xy} + 5\sqrt[4]{3xy} - 4\sqrt[4]{3xy}$

Simplifying $5\sqrt[3]{y} + 4\sqrt[3]{y}$ and $7\sqrt[4]{x} - 2\sqrt[4]{y}$

In $15\sqrt[4]{2x} + 3\sqrt[4]{2x}$, what stays the same when you combine the terms?

In $5\sqrt[3]{2x}$, match each part to its name.

Put these steps in order to combine radicals that don't look alike at first, like $3\sqrt[4]{16x} + 2\sqrt[4]{x}$.

To simplify $12\sqrt[4]{3x} + 5\sqrt[4]{3x}$, add the _____ of the like radicals to get $17\sqrt[4]{3x}$.

Two radicals must have the same what to be called 'like radicals' and combined by addition or subtraction?

To simplify a radical, what type of factor should you extract from the radicand?

True or False: $7\sqrt[3]{2} + 5\sqrt[3]{2} = 12\sqrt[3]{4}$

Look at $9\sqrt[4]{42x}$ and $2\sqrt[4]{42x}$. Name the two conditions that make these like radicals, then find their sum.