Square Roots

Exponentiation and Square Roots

Exponentiation

• Definition: Exponentiation is a mathematical operation that involves raising a base number to a certain power.

  • Example: (5^2) is read as "five squared."

  • It consists of multiplying the base number by itself as many times as indicated by the exponent.

  • For instance, (5^2 = 5 \times 5 = 25).

Square Roots

• Definition: The square root of a number is the inverse operation of squaring.

  • It determines which number multiplied by itself yields the original number.

  • Symbol: The square root is denoted by the radical sign (√).

• To find the square root of a number (x), you need to find a number (y) such that:

  • (y \times y = x) or equivalently, (y^2 = x).

Examples of Square Roots

1. Example 1: (\sqrt{25})

   • Calculation: Find the number (y) such that (y^2 = 25).

   • Solution: (5 \times 5 = 25), thus (\sqrt{25} = 5).

2. Example 2: (\sqrt{169})

   • Calculation: Find the number (y) such that (y^2 = 169).

   • Solution: (13 \times 13 = 169), thus (\sqrt{169} = 13).