Differentiate Between Exponents and Roots
Exponents are tiny numbers on the upper right side of a larger number. Roots are represented by a number inside the radical symbol √.
Exponents
Exponents are super easy to work. The small-sized number (exponent) represents how many times you multiply the larger-sized number (base) by itself.
If the exponent is 2, then that is squaring a number. If the exponent is 3, then it called a cube. Exponents higher than that are referred to as the “nth power”. For example, 35 would be 3 to the 5th power.
Square Roots
Just like with exponents, roots can be squares, cubes, and beyond. A square root will just be represented with just the root symbol, but anything bigger will have a smaller number to the outside left of the symbol representing the power. For now, we only have to focus on square roots. In geometry, we will deal more with cubes.
To solve a square root, you determine which number multiplied by itself would equal the number inside the radical. For example, the square root of 25 is 5 because 5 * 5 = 25.
Simplify Radicals
What if the problem is not a perfect square? It could possibly still be simplified. If the number inside the radical has two factors where one is a perfect square, then the problem can be simplified. For example, 12 contains the factors 1, 2, 3, 4, 6, and 12. Which of these factors is a perfect square? That’s right! 4 is a perfect square. Divide 12 by 4 to get the other factor that we will need: 3. Put both the 4 and 3 under a separate radical: √4 and √3. Next,get the square root of 4, which is 2. The number 3 cannot be simplified any further so it stays under the radical. Your final answer is: 2√3.
