Nt1320 Unit 3

o Compare the parts of an exponential expression with a radical expression.

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.
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|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 (there is radical sign) |
| |
|(3) In rationalizing a denominator, we multiply and divide the expression by the rationalizing factor of the denominator surd so that the denominator turns into a |
|rational number. |
|For example, 4/√5 is rationalized as follows: |
|4/√5 = (4/√5)(√5 / √5) = 4 √5 / (√5 * √5) = 4 √5 /25 |
|and |
|3/(√a + √b) is rationalized as follows: |
|3/(√a + √b) = [3/(√a + √b)][(√a - √b)/(√a - √b)] = 3(√a - √b) / [(√a + √b)(√a - √b)] = 3(√a + √b)/(a - b). |