square root of x 2 x 4

Guri Bee

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20-10-2024

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Demystifying the Square Root of (x^2)(x4): A Step-by-Step Guide

The expression "square root of (x^2)(x4)" might look intimidating at first glance, but it's actually quite straightforward to solve. This article will break down the process step by step, providing a clear understanding of the concepts involved.

Understanding the Basics:

• Square root: The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3 because 3 x 3 = 9.
• Exponents: Exponents represent repeated multiplication. In the expression (x^2)(x4), 'x^2' means 'x multiplied by itself twice' (x * x) and 'x^4' means 'x multiplied by itself four times' (x * x * x * x).

Solving the Expression:

1. Simplify the expression inside the square root:
   • (x^2)(x4) can be simplified using the rule of exponents that states: x^m * x^n = x^(m+n). Therefore: (x^2)(x4) = x^(2+4) = x^6
2. Find the square root of x^6:
   • The square root of x^6 is x^3. This is because x^3 * x^3 = x^6.

Therefore, the square root of (x^2)(x4) is x^3.

Practical Example:

Let's say x = 2.

• Original expression: √(x^2)(x4) = √(2²⁾⁽²4)
• Simplify: √(2²⁾⁽²4) = √(4 * 16) = √64
• Calculate the square root: √64 = 8

In this example, we can see that when x = 2, the square root of (x^2)(x4) equals 8.

Important Note:

It's crucial to remember that the solution (x^3) is only valid when x is a non-negative number. This is because the square root of a negative number is not a real number.

Let's explore some common questions:

• Q: Can the expression be simplified further?

  • A: No, x^3 is the simplest form of the expression.

• Q: What if the expression was (x^3)(x5)?

  • A: We would use the same principles. (x^3)(x5) = x^(3+5) = x^8. The square root of x^8 is x^4.

In Conclusion:

Understanding the principles of exponents and square roots allows us to simplify seemingly complex expressions like the square root of (x^2)(x4). By breaking down the problem into manageable steps and using the appropriate rules, we can arrive at the correct solution.