Multiplying Radical Expressions – Practice Problems

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When multiplying radical expressions, it is important to check if the given radicals have the same index (the number at the upper left of the radical symbol) or not. This is because the only radicals which can be simplified further when multiplied together are those which have the same index.

To multiply radical expressions with the same index just separately multiply their radicands (the number inside the radical symbol) and coefficients (the number outside the radical symbol). Then simplify and combine the two products if possible.

For example, consider the radicals (3√2) and (5√8). When multiplying the two, you get 15√16, since 16 is a perfect square whose square root is 4. Then multiplying 4 by 15 gives a final answer of 60.

Expressions and Equations Work with radicals and integer exponents.


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Exercises in this Practice Problem
Explain how to multiply $(15\sqrt5+5\sqrt3)(6\sqrt3-2\sqrt5)$.
Calculate $(15\sqrt5+5\sqrt3)(6\sqrt5-2\sqrt3)$.
Identify the steps of multiplication.
Calculate the product.
Decide which expressions can be simplified.
Find the errors in the calculation.