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(3√2)2: Understanding the Exponentiation of Radical Expressions
In mathematics, radicals and exponents are two fundamental concepts that are used to simplify and manipulate algebraic expressions. In this article, we will explore the evaluation of the expression (3√2)2, which involves the combination of radicals and exponents.
What is the meaning of (3√2)2?
The expression (3√2)2 can be read as "three square root of two squared." In other words, it is the result of multiplying three times the square root of two, and then squaring the entire expression.
How to evaluate (3√2)2?
To evaluate (3√2)2, we need to follow the order of operations (PEMDAS):
- ** Evaluate the radical expression**:
3√2 = 3 × √2 - ** Square the entire expression**:
(3√2)2 = (3√2) × (3√2)
Using the properties of radicals, we can simplify the expression:
3√2 = 3 × √2 = 3 × √(2) = 3 × (√2)
Now, let's square the entire expression:
(3√2)2 = (3 × √2) × (3 × √2) = 9 × (√2) × (√2) = 9 × 2 = 18
Therefore, the final answer is:
(3√2)2 = 18
Importance of (3√2)2 in Real-Life Applications
The expression (3√2)2 may seem like a simple mathematical expression, but it has numerous applications in various fields, including:
- Physics: In physics, radicals and exponents are used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
- Engineering: In engineering, radicals and exponents are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
- Computer Science: In computer science, radicals and exponents are used in algorithms for data compression, encryption, and machine learning.
In conclusion, the expression (3√2)2 is a simple yet powerful mathematical expression that has far-reaching implications in various fields. By understanding how to evaluate this expression, we can unlock the secrets of mathematics and apply them to real-world problems.
