5.2.1 Perfect Squares Revisited

Algebra 15.2.1 Perfect Squares Revisited

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Warm Up

What is the value of $4 \times 4$ ?

Compare your answer:

What is the value of $4^{2}$ ?

Compare your answer:

Using what you know about roots, what is the value of $\sqrt{16}$ ?

Compare your answer:

Talk to a partner. How can you prove $\sqrt[2]{4^{2}} = 4$ ?

Your answers may vary, but here is an example:

Since $4^{2} = 4 \cdot 4 = 16$ and $\sqrt{16} = 4$ , $\sqrt[2]{4^{2}} = 4$ .

Notice that the root and exponents are the same and simplify to leave the integer only.

Talk to a partner. What do you think the answer to $\sqrt[5]{4^{5}}$ would be?

Your answers may vary, but here is an example:

$\sqrt[5]{4^{5}} = 4$

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
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- Section URL: https://openstax.org/books/algebra-1/pages/5-2-1-perfect-squares-revisited

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