What is the fourth root of 81?
Understand the Problem
The question is asking for the fourth root of the number 81. To find this, we can express 81 in exponential form and then apply the concept of roots.
Answer
The fourth root of 81 is \( 3 \).
Answer for screen readers
The fourth root of 81 is ( 3 ).
Steps to Solve
- Express 81 in Exponential Form
To find the fourth root of 81, we can first express 81 as a power of 3: $$ 81 = 3^4 $$
- Apply the Fourth Root
Now, we need to find the fourth root of 81. Using the property of exponents, we can express this as: $$ \sqrt[4]{81} = \sqrt[4]{3^4} $$
- Simplify the Expression
We can simplify the fourth root of $3^4$ directly: $$ \sqrt[4]{3^4} = 3 $$
Thus, the fourth root of 81 is 3.
The fourth root of 81 is ( 3 ).
More Information
The fourth root means finding a number that, when multiplied by itself four times, gives the original number. In this case, ( 3 \times 3 \times 3 \times 3 = 81 ). This shows the inverse of exponentiation and roots in mathematics.
Tips
- Misinterpreting the fourth root as just dividing the exponent by 4, rather than applying the root correctly.
- Confusing the base and the exponent during the simplification process.
