Find the square root of 96.(1 point)
Responses
166–√
16 start root 6 end root
64–√
6 start root 4 end root
46–√
4 start root 6 end root
24
√96 is approximately equal to 9.798.
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
212−−√
2 start root 12 end root
46–√
The cubic root of 96 is approximately equal to 4.58.
Find the cubic root of 189.(1 point)
Responses
277–√3
27 root index 3 start root 7 end root
921−−√3
9 root index 3 start root 21 end root
37–√3
3 root index 3 start root 7 end root
37–√
The cubic root of 189 is approximately equal to 5.79.
To find the square root of 96, we need to determine the closest perfect square to 96. The perfect squares that are smaller than 96 are 64 (8^2) and 81 (9^2). Since 64 is the closest, we can use that as a reference.
To find the square root of 96, we need to divide 96 by 64. This gives us a quotient of 1 and a remainder of 32.
Next, we bring down the next two digits of 96, which are 00. We double the quotient we found earlier (1*2 = 2) and write it as our next digit.
Now, we need to find a number to place after the 2 so that, when we multiply it by the new number formed (22), the product is less than or equal to 3200 (the number remaining). We can see that 6 * 26 equals 156, which is smaller than 3200. So, we write 6 as the next digit.
Now, we repeat the process. We bring down the next two digits of 96, which is 96. We double the whole number we have so far (126) to get 252 as our next approximation.
Lastly, we need to find the number that, when multiplied by itself, is close to 9696 (the remaining number). We can see that 7 * 273 equals 1911, which is smaller than 9696. So, we write 7 as the next digit.
Putting it all together, the square root of 96 is approximately 9.798.
Therefore, the correct response is option: 9.798