# Mat117 Compare Exponential Expressions

o Explain what a perfect square is and give some examples.

o Describe the process of rationalizing the denominator

|(1) Consider the exponential expression 3^(1/2). This has base 3 and an exponent 1/2. | |The denominator of the exponent is 2. This is the order. | | The equivalent radical expression is √3. Here, √ is called the radical sign. 3 is called the radicand. Since √3 means square root of 3, the order is 2. | | Another example is 10^(1/3). This has base 10 and an exponent 1/3. | |The denominator of the exponent is 3. This is the order. | | The equivalent radical expression is 3√10 (The 3 is over the radical sign). 10 is the radicand. Since 3√10 means cube root of 10, the order is 3. | | | |(2) A perfect square is a number whose square root is a whole number. For example, 25 and 64 are prefect squares since √25 = 5 and √64 = 8 are both whole numbers. | |On the other hand 15 is not a perfect square since √15 = 3.87 is not a whole number. | |In Algebra also, a perfect square expression is one whose square root will have no radical sign anywhere in it. For example, x^2 is a perfect square because its | |square root is x (no radical sign here). On the other hand, x^3 is not a perfect square because √(x^3) = x √x...

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