C5a
Practice - Roots
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. What is -27 (raised to the 2/3 power)?
2. Simplify 6 (raised to the 1/2 power) + 24 (raised to the 1/2 power) + 27 (raised to the 1/3 power).
3. What is √(625)? What is √(1200)?
4. What is √(242)? Use the built-in calculator and round to the nearest thousandth.
ANSWERS
1. The 2/3 power means the square of the cube root. The cube root of - 27 is -3. The square of this is 9, which is the answer.
2. The √(24) is √(4 x 6). This is 2 times √(6). The ³√ (27) is 3. So the answer is (1 x √(6) + (2 x √(6) + 3 = 3 √(6) +3.
3. Use the built-in calculator. √(625) = 25. √(1200) = 34.64.
4. 15.556. Use the built-in calculator.
CALCULATOR STEPS USING ROOTS
In addition to the calculator keys used in the preceding pages, this page uses the sqrt and xrt keys. (Sqrt is the combination of the 2nd and x² keys. xrt is the combination of 2nd and exp keys.)
1. Press on and clear. Press ( . Press (-) . Key in 27. Press ) . Press exp. Press n/d. Key in 2. Press down. Key in 3. Press right. Press enter. The screen should show "9". Be sure to enter ( ) around the -27.
2. Press on and clear. Press 2nd and x². Key in 6. Press right. Press + . Press 2nd and x². Key in 24. Press right. Press + . Key in 3. Press 2nd and exp. Key in 27. Press right. Press enter. The screen should show "3 √ 6 + 3".
3. Press on and clear. Press 2nd and x² . Key in 625. Press enter. The screen should show "25". Press clear. Press 2nd and x² . Key in 1200. Press enter. The screen should show "34.641", rounded to the thousandth place.
4. Press on and clear. Press 2nd and x² . Key in 242. Press enter. The screen should show "11 √ 2". Press <> . The screen should show "15.556", rounded to the nearest thousandth.
CALCULATOR STEPS USING POWERS
1. Press on and clear. Press ( . Key in (-) . Key in 27. Press ) . Press exp . Press n/d. Key in 2. Press down. Key in 3. Press right. Press enter. The screen should show "9". Be sure to enter ( ) around the -27.
2. Same as in the previous section.
3. Press on and clear. Key in 625. Press exp . Press n/d . Key in 1 . Press down. Key in 2. Press right. Press enter. The screen should show "25". Press on and clear. Key in 1200. Press exp . Press n/d . Key in 1. Press down. Key in 2 . Press right. Press enter. The screen should show "34.641", rounded to the nearest thousandth.
4. Press on and clear. Key in 242. Press exp . Press n/d . Key in 1 . Press down. Key in 2. Press right. Press enter. The screen should show "15.556", rounded to the nearest thousandth.