Find the square root of 96.(1 point) Responses 166–√ 16 start root 6 end root 24 24 46–√ 4 start root 6 end root 64–√
The square root of 96 is between 9 and 10.
Find the square root of 96.(1 point) Responses 166–√ 16 start root 6 end root 24 24 46–√ 4 start root 6 end root 64–√
The square root of 96 is approximately 9.8.
Nope
Apologies for the incorrect response earlier. Let's calculate the square root of 96 step by step:
1. We can express 96 as the product of its prime factors: 96 = 2^5 * 3^1.
2. Now we can use the property of square roots that states √(a*b) = √a * √b.
Applying this property to our expression, we have √2^5 * 3^1 = √2^4 * 2 * 3^1.
Simplifying further, we get 2^2 * √2 * √3 = 4 * √2 * √3.
3. Both √2 and √3 are irrational numbers, so we can't simplify them further.
4. By multiplying, we have 4 * √2 * √3 = 4√6.
Therefore, the square root of 96 is 4√6.
Find the cubic root of 96.(1 point) Responses 27–√3 2 root index 3 start root 7 end root 212−−√3 2 root index 3 start root 12 end root 212−−√ 2 start root 12 end root 46–√
To find the cubic root of 96, we need to find a number that, when multiplied by itself three times, equals 96.
Estimating, we know that the cubic root of 64 is 4 because 4 * 4 * 4 = 64.
Let's try a number slightly larger than 4. If we cube 5 (5 * 5 * 5), we get 125, which is larger than 96.
Now, let's try a number slightly smaller than 5. If we cube 4.5 (4.5 * 4.5 * 4.5), we get 91.125, which is less than 96.
Thus, the cubic root of 96 is between 4.5 and 5.
nope
Apologies for the incorrect response earlier. Let's calculate the cubic root of 96 step by step:
1. To find the cubic root of 96, we want to find a number that, when raised to the power of 3, equals 96.
2. We can use an estimation method to figure out the closest integer value for the cubic root.
3. Start by estimating a value for the cubic root of 96. Let's choose 4.
4. Calculate 4^3 = 4 * 4 * 4 = 64. Since 64 is less than 96, we know that our estimate of 4 is too low.
5. Let's try a larger value, 5.
6. Calculate 5^3 = 5 * 5 * 5 = 125. Since 125 is greater than 96, we know that our estimate of 5 is too high.
7. Now we can refine our estimation by choosing a value between 4 and 5, such as 4.5.
8. Calculate 4.5^3 = 4.5 * 4.5 * 4.5 = 91.125. Since 91.125 is still less than 96, we know that our estimate of 4.5 is too low.
9. We can continue this process, gradually narrowing down the range and obtaining more accurate estimates.
Based on this estimation process, the cubic root of 96 is between 4.5 and 5.