Lesson 5

Self-Check 1

Rationalize the denominator in the following radical expressions.

1. Answer
   
   
2. Answer
   
   
3. Answer
   
   
4. Answer
   
   
5. The highest diving platforms at pools are 10 m above the water. The time a diver takes to hit the water in a pool is the same as diving off a cliff, and can be calculated using the radical equation
   
   The distance is d = −10 m, and a, the acceleration due to gravity, is −9.81 m/s2. The negative numbers indicate the direction is downward. Use the general rule to rewrite the expression with a radical in the numerator and a radical in the denominator; then rationalize the denominator. Answer

When you square a negative number, the result is always positive; for example, (−5)2 = 25. The square root sign, however, indicates only the principal square root (or the positive square root) = 5 not −5. You likely noticed in this lesson that when diving into the ocean or into swimming pools, the distances were negative. In physics, positive and negative numbers indicate direction—positive is up, and negative is down. The distances have to be negative numbers because you can’t dive upwards into the water.

There may be times when you know that you want to have a negative value for an answer even though you are working with square roots. The negative square root is also called the secondary square root. When calculating expressions, how do you indicate that you want the secondary square root or negative root? How do you indicate that you want both the principal and secondary (positive and negative) square roots? You can use symbols in front of the radical signs to indicate exactly what you are looking for.

Self-Check 2

Write the square root expression that is equal to each of the following numbers.

1. −4
   
   
2. ±8
   
   
3. ±x3
   
   
4. −ay4

Answers