Which Term Is A Perfect Square Of The Root 3 X 4 3x^4 3 X 4 ?A. 6 X 8 6x^8 6 X 8 B. 6 X 16 6x^{16} 6 X 16 C. 9 X 8 9x^8 9 X 8 D. 9 X 16 9x^{16} 9 X 16

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Introduction

In mathematics, a perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it can be expressed as 4^2. In algebra, we can also have perfect squares of variables and expressions. In this article, we will explore which term is a perfect square of the root 3x43x^4.

Understanding Perfect Squares

A perfect square is a number or expression that can be expressed as the square of another number or expression. For example, (2x)^2 is a perfect square because it can be expressed as 4x^2. To find the perfect square of an expression, we need to multiply the expression by itself.

Finding the Perfect Square of 3x43x^4

To find the perfect square of 3x43x^4, we need to multiply it by itself. This means we need to multiply 3x43x^4 by 3x43x^4.

Step 1: Multiply 3x43x^4 by 3x43x^4

To multiply 3x43x^4 by 3x43x^4, we need to follow the rules of exponentiation. When we multiply two variables with the same base, we add their exponents. In this case, we have:

(3x^4) * (3x^4) = 3 * 3 * x^4 * x^4 = 9 * x^(4+4) = 9 * x^8

Step 2: Simplify the Expression

The expression 9 * x^8 is already simplified. We can see that it is a perfect square of the root 3x43x^4.

Conclusion

In conclusion, the perfect square of the root 3x43x^4 is 9 * x^8. This means that option C, 9x^8, is the correct answer.

Comparison of Options

Let's compare the options:

A. 6x^8: This option is not a perfect square of the root 3x43x^4 because it does not have the same base and exponent as the original expression.

B. 6x^16: This option is not a perfect square of the root 3x43x^4 because it has a different base and exponent than the original expression.

C. 9x^8: This option is a perfect square of the root 3x43x^4 because it has the same base and exponent as the original expression.

D. 9x^16: This option is not a perfect square of the root 3x43x^4 because it has a different base and exponent than the original expression.

Final Answer

Introduction

In our previous article, we explored which term is a perfect square of the root 3x43x^4. In this article, we will answer some frequently asked questions about perfect squares and roots.

Q: What is a perfect square?

A: A perfect square is a number or expression that can be expressed as the square of another number or expression. For example, (2x)^2 is a perfect square because it can be expressed as 4x^2.

Q: How do I find the perfect square of an expression?

A: To find the perfect square of an expression, you need to multiply the expression by itself. For example, to find the perfect square of 3x43x^4, you would multiply it by itself: (3x^4) * (3x^4) = 9 * x^8.

Q: What is the difference between a perfect square and a perfect cube?

A: A perfect square is a number or expression that can be expressed as the square of another number or expression. A perfect cube is a number or expression that can be expressed as the cube of another number or expression. For example, (2x)^3 is a perfect cube because it can be expressed as 8x^3.

Q: Can a perfect square have a negative exponent?

A: Yes, a perfect square can have a negative exponent. For example, (2x)^(-2) is a perfect square because it can be expressed as 1/(4x^2).

Q: How do I simplify a perfect square expression?

A: To simplify a perfect square expression, you need to follow the rules of exponentiation. When you multiply two variables with the same base, you add their exponents. For example, (3x^4) * (3x^4) = 9 * x^8.

Q: Can a perfect square have a fractional exponent?

A: Yes, a perfect square can have a fractional exponent. For example, (2x)^(1/2) is a perfect square because it can be expressed as sqrt(2x).

Q: How do I find the square root of a perfect square expression?

A: To find the square root of a perfect square expression, you need to take the square root of the expression. For example, the square root of (3x4)2 is 3x^2.

Q: Can a perfect square have a complex number as its base?

A: Yes, a perfect square can have a complex number as its base. For example, (2+3i)^2 is a perfect square because it can be expressed as (2+3i)(2+3i).

Conclusion

In conclusion, perfect squares and roots are an important concept in mathematics. By understanding how to find perfect squares and simplify expressions, you can solve a wide range of mathematical problems.

Frequently Asked Questions

  • Q: What is a perfect square?
  • A: A perfect square is a number or expression that can be expressed as the square of another number or expression.
  • Q: How do I find the perfect square of an expression?
  • A: To find the perfect square of an expression, you need to multiply the expression by itself.
  • Q: What is the difference between a perfect square and a perfect cube?
  • A: A perfect square is a number or expression that can be expressed as the square of another number or expression. A perfect cube is a number or expression that can be expressed as the cube of another number or expression.

Glossary

  • Perfect square: A number or expression that can be expressed as the square of another number or expression.
  • Perfect cube: A number or expression that can be expressed as the cube of another number or expression.
  • Square root: The number or expression that, when multiplied by itself, gives the original number or expression.
  • Exponent: A small number that is written above and to the right of a variable or number, indicating how many times the variable or number should be multiplied by itself.