Radical Sign

Definition

The radical sign, also known as the square root symbol, is a mathematical symbol used to represent the square root of a number. It is a key concept in understanding and working with square roots, which are essential in simplifying and using square roots in various algebraic operations.

5 Must Know Facts For Your Next Test

1. The radical sign is used to represent the square root of a number, which is the value that, when multiplied by itself, gives the original number.
2. When simplifying square roots, the goal is to remove any perfect squares from the radicand, leaving only the smallest possible number under the radical sign.
3. Dividing square roots involves using the property that $\sqrt{a} \div \sqrt{b} = \sqrt{a/b}$, where $a$ and $b$ are positive real numbers.
4. The square root of a negative number is not a real number, but rather an imaginary number, which is represented using the symbol $i$, where $i^2 = -1$.
5. The radical sign can be used to represent the square root of a variable, which is useful in solving various algebraic equations and expressions.

Review Questions

• Explain how the radical sign is used in the context of simplifying square roots (Topic 9.2)
  • When simplifying square roots, the goal is to remove any perfect squares from the radicand, leaving only the smallest possible number under the radical sign. This is done by factoring the radicand and identifying any perfect squares that can be taken out of the radical. For example, $\sqrt{72}$ can be simplified to $6\sqrt{2}$ by identifying that $72 = 4 \times 18$, and $4$ is a perfect square that can be removed from the radical.
• Describe the process of dividing square roots (Topic 9.5)
  • Dividing square roots involves using the property that $\sqrt{a} \div \sqrt{b} = \sqrt{a/b}$, where $a$ and $b$ are positive real numbers. This means that to divide two square roots, you can simply divide the radicands and then take the square root of the result. For example, $\sqrt{50} \div \sqrt{8} = \sqrt{50/8} = \sqrt{25/4} = \sqrt{25} \div \sqrt{4} = 5 \div 2 = 2.5$.
• Analyze the relationship between the radical sign and perfect squares (Topic 9.1)
  • The radical sign is closely related to perfect squares, as a perfect square is a number that can be expressed as the product of two equal integers. When the radicand is a perfect square, the square root can be easily calculated without the use of a radical sign. For example, the square root of $16$ is $4$, as $4 \times 4 = 16$. Understanding the concept of perfect squares is crucial in simplifying square roots, as the goal is to remove any perfect squares from the radicand, leaving only the smallest possible number under the radical sign.

Related terms

Square Root:

The square root of a number is the value that, when multiplied by itself, gives the original number. The radical sign is used to represent the square root of a number.

Radicand:

The radicand is the number or expression inside the radical sign, which represents the value whose square root is being calculated.

Perfect Square:

A perfect square is a number that can be expressed as the product of two equal integers. The square root of a perfect square can be easily calculated without the use of a radical sign.