a. Evaluate √36. b. Evaluate √9 · √4. c. Is it true that √36 = √9 · √4?

Understand the Problem

The question involves evaluating square roots and assessing an equation related to square roots. Specifically, it asks to compute √36, √9 · √4, and to verify if √36 equals √9 · √4.

Answer

Yes, $ \sqrt{36} = \sqrt{9} \cdot \sqrt{4} = 6 $.

Steps to Solve

Evaluate ( \sqrt{36} )

To find the square root of 36, we look for a number that, when multiplied by itself, equals 36. The answer is: $$ \sqrt{36} = 6 $$

Evaluate ( \sqrt{9} \cdot \sqrt{4} )

Next, we calculate the individual square roots and then multiply:

For ( \sqrt{9} ), we get ( 3 ) because ( 3 \times 3 = 9 ).
For ( \sqrt{4} ), the answer is ( 2 ) since ( 2 \times 2 = 4 ).

Now, multiply them: $$ \sqrt{9} \cdot \sqrt{4} = 3 \cdot 2 = 6 $$

Verify if ( \sqrt{36} = \sqrt{9} \cdot \sqrt{4} )

We found that ( \sqrt{36} = 6 ) and ( \sqrt{9} \cdot \sqrt{4} = 6 ). So we can write: $$ \sqrt{36} = \sqrt{9} \cdot \sqrt{4} $$ Thus, this statement is true.

a. ( \sqrt{36} = 6 )
b. ( \sqrt{9} \cdot \sqrt{4} = 6 )
c. Yes, ( \sqrt{36} = \sqrt{9} \cdot \sqrt{4} = 6 )

More Information

The square root function retrieves the principal (non-negative) root of a number. In this case, both evaluations yield the same result, demonstrating the property of square roots that states ( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} ).

Tips

Confusing the concept of square roots can lead to incorrectly calculating ( \sqrt{a} ) or assuming both multiplication and addition will yield similar results. Always remember that multiplication applies differently in square roots.

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