Square Roots and Cube Roots

Transcription

1 Domain 2 Leon 6 Square Root and Cube Root Common Core Standard: 8.EE.2 Getting the Idea Squaring a number mean raiing it to the power of 2. For example, 7 2 i equivalent to 7 7, or 49. So, we ay that 49 i a perfect quare. The oppoite, or invere, of quaring a number i taking it quare root. We ue the radical ymbol (œw ) to repreent quare root. To find the quare root of a perfect quare, think about what number, when multiplied by itelf, will reult in that perfect quare. Example 1 Solve for y. y Strategy Determine what number, multiplied by itelf, reult in 196. Step 1 Take the quare root of both ide of the equation. The oppoite of quaring a number i taking it quare root. y y Step 2 Try quaring number until you find one that reult in Too low Too low Step Solve for y , o y Solution Since , y

2 Cubing a number mean raiing it to the power of. For example, 2 i equivalent to 2 2 2, or 8. So, we ay that 8 i a perfect cube. The oppoite, or invere, of cubing a number i taking it cube root. We ue the ymbol to repreent cube root. To find the cube root of a perfect cube, think about what number, when cubed, will reult in that perfect cube. Example 2 Solve for r. r Strategy Determine what number, when cubed, reult in 125. Step 1 Take the cube root of both ide of the equation. The oppoite of cubing a number i taking it cube root. r r Step 2 Try cubing number until you find one that give a reult of 125. You already know that Start with Step Solve for r , o r Solution r 5 5 Since , r 5 5. Too low Too low The number under a radical ign i called the radicand. If you do not have a calculator handy, you may need to etimate the value of a quare root or a cube root. To etimate a quare root, find the two perfect quare between which the radicand lie. Take the quare root of each to find the range of your etimate. To etimate a cube root, find the two perfect cube between which the radicand lie. Then take the cube root of each to find the range of your etimate. 60 Domain 2: Expreion and Equation

3 Leon 6: Square Root and Cube Root Example Between which two conecutive integer i 500? Strategy Step 1 Step 2 Solution Find the two perfect cube between which 500 lie. Then take the cube root of each to make your etimate. Try cubing conecutive poitive integer. You know from Example 2 that Start with The radicand, 500, i between the perfect cube 4 and 512. Etimate the value of , 500, 512 7, 500, ha a value between 7 and 8. Root can help you olve meaurement problem, uch a problem involving the area of a quare or the volume of a cube. Coached Example The area of the quare garden on the right i 121 quare yard. What i the length,, of each ide of the garden? The formula for finding the area, A, of a quare i A 5 2, where i the length of a ide. The area of the garden above i quare yard. To find the length of one ide, take the root of that area. On the line below, try quaring number until you find one that reult in. That i the value of. The length of each ide,, of the garden i yard. Garden 61

4 Leon Practice Chooe the correct anwer. 1. What i the value of 100? A. 4 B. 10 C. 25 D What i the value of 27? A. B. 5 C. 9 D Solve for y. 4. Between which two conecutive integer i 11? A. 0 and 1 B. 1 and 2 C. 2 and D. 4 and 5 5. Solve for x. x A. x 5 6 B. x 5 15 C. x 5 16 D. x y A. y 5 4 B. y 5 6 C. y 5 7 D. y Between which two conecutive integer i 200? A. 66 and 67 B. 20 and 21 C. 6 and 7 D. 5 and 6 62 Domain 2: Expreion and Equation

5 Leon 6: Square Root and Cube Root 7. Which tatement below i true? A B. 2 5 C D Which tatement below i true? A B C D The wooden block hown below i a cube. It ha a volume of 512 cubic centimeter. A. What i the length of one ide,? (Hint: the formula for the volume, V, of a cube i V 5.) Show your work. B. Indira want to paint the front face of the block. What i the area of one of the face? Show your work. 6

6 10. Ue the expreion hown below to label the point on the number line Select True or Fale for each equation. A True Fale B True Fale C True Fale D. 9 5 True Fale 12. Draw a line from each quare root or cube root to it value. A B C D Look at each quare root or cube root. I it equivalent to 4? Select Ye or No. A. 8 Ye No B. 64 Ye No C. 16 Ye No D. 12 Ye No 64 Domain 2: Expreion and Equation

7 Leon 6: Square Root and Cube Root 14. Determine whether each quare root or cube root ha a value greater than 10 or le than 10. Write the root in the correct box , Le than 10 Greater than Circle the number that make each equation true ,