Identify Roots Quick Check 1 of 51 of 5 Items Question Find the square root of 96.(1 point) Responses 166–√ 16 start root 6 end root 46–√ 4 start root 6 end root 24 24 64–√
The square root of 96 is √96 = 4√6
Find the cubic root of 96.(1 point) Responses 212−−√3 2 root index 3 start root 12 end root 27–√3 2 root index 3 start root 7 end root 46–√ 4 start root 6 end root 212−−√
Find the cubic root of 189.(1 point) Responses 37–√ 3 start root 7 end root 277–√3 27 root index 3 start root 7 end root 37–√3 3 root index 3 start root 7 end root 921−−√3
The cubic root of 189 is ∛189 = 3∛7
Find the square root of 250.(1 point) Responses 510−−√ 5 start root 10 end root 250 250 105–√ 10 start root 5 end root 2510−−√
The square root of 250 is √250 = 5√10
Find the square root of 128.(1 point) Responses 64 −−−√ x 2–√ start root 64 end root x start root 2 end root 42–√ 4 start root 2 end root 82–√ 8 start root 2 end root 24–√ 2 start root 4 end root
The square root of 128 is √128 = 8√2
To find the square root of 96, follow these steps:
1. Start by writing down the number 96.
2. Look for a perfect square that is a factor of 96. The largest perfect square that is less than 96 is 64 (8 squared).
3. Divide 96 by 64: 96 ÷ 64 = 1 remainder 32.
4. Now we have the incomplete square root: √64 with a quotient of 1.
5. Bring down the next two digits of the remaining number (32) to continue the process.
6. Double the quotient (in this case, 1) and write it on the left: 1 × 2 = 2.
7. Determine the largest possible digit to fill the blank that, when multiplied by the result from Step 6, gives a result less than or equal to 32. In this case, it is 6.
8. Write 6 on the right side, as the result: 6.
9. Subtract the product of the result from Step 7 (6) and the doubled quotient (2 × 6 = 12) from the remaining number (32 - 12 = 20).
10. Bring down the next two digits of the remaining number (20) and continue the process.
11. Double the new quotient (26) and write it on the right side: 26 × 2 = 52.
12. Determine the largest possible digit to fill the blank that, when multiplied by the result from Step 11, gives a result less than or equal to 20. In this case, it is 4.
13. Write 4 on the right side, after the previous result: 64.
14. Subtract the product of the result from Step 13 (64) and the new quotient (26), from the remaining number (20 - 64 = -44).
15. Since we have finished the process and the remaining number is negative, we know that the square root is not a whole number.
16. Therefore, the square root of 96 is an irrational number, approximately equal to 9.79796.
So, the correct response is: 9.79796