Question

What is the quartic root of 64? And how did you figure it out? I'm really confuse on quartic roots.

Answer 1

The quartic root of 64 is found by first taking the square root of 64, which is 8, and then taking the square root of that result, which gives an answer between 2 and 3. Since 3 raised to the fourth power (3²²) is 81, which is closest to 64, the quartic root of 64 is 3.

Step-by-step explanation:

The quartic root of 64 is determined by finding a number that when multiplied by itself four times yields 64. This can be calculated by taking the square root twice or by raising the number to the power of 0.25. To find the quartic root of 64, we can follow these steps:

1. First, take the square root of 64: √64 = 8.
2. Then, take the square root of the result: √8 = 2.828427124746 (approximately).
3. Since we are looking for a whole number and we know that 2² = 4 and 3² = 9, it's clear that the square root of 8 is between 2 and 3. However, as 2²² = 16 and 3²² = 81, the integer number we are interested in is 2 because 2²² = 2*2*2*2 = 16, which is less than 64. By trying the next integer, 3, we find that 3²² = 3*3*3*3 = 81, which is greater than 64.
4. Hence, we can infer that the quartic root of 64 is 3 because 3²² = 3*3*3*3 = 81 and that is the closest integer quartic root we can find for 64.

Note: In cases where precision is crucial, and the result doesn't need to be an integer, the calculator method is most accurate. For an integer result, it can be helpful to use knowledge of small powers of integers.

Answer 2

`\sqrt[4]{64} = \sqrt{ \sqrt{ 8^(2) } } = √(8) =2 √(2) .`