Algebra I – Powers and Roots

Squaring a number is multiplying a number by itself. Squaring a negative number always give a positive result. 

Raising to powers such as squaring, cubing, raising to the fourth, and so on. How many times you are multiplying is called an exponent and a number being multiplied by itself is called the Base. Raising a negative number to even power gives you a positive result, while raising negative number to odd powers give you a negative result. Zero raised to any power equal zero, one raised to any power equal one and raising any number to the first power give you that number back. 

Square roots, work backwards to find the number that was squared. Squaring a negative number get positive result, square roots are always defined as being positive.

Do negative numbers even have square roots? Whenever you square a number you get a positive result or zero. Negative number doesn’t have square roots. But its later lesson when negatives have square roots that are imaginary numbers. 

Cube roots and beyond (cube roots, fourth roots, fifth roots, and so on …). Square roots of negative numbers are not real (they don’t exist). All roots of positive numbers are real (they exist). Even roots of negative numbers are not real. 

PEMDAS (parentheses, exponents, then multiplication and division at the same time from left to right, and then addition and subtraction together from left to right). Order of operations, now with exponents!

If the exponent is 2, we can call a square and exponent is 3 we can call a cube.

If negative numbers are involved, please see its associate the exponent with the correct base by parentheses group a negative number raised to some power.

When a negative base raised to an even power is positive and a negative base raised to an odd power is negative.

To find the square root of a number is just find a number that when squared results in the original number.

In these videos lesson we are going to learn:

- Squaring a number: Multiplying a number by itself
- Raising to powers: Squaring, cubing, raising to the fourth, and so on...
- Square roots: Work backwards to find the number that was squared
- Roots of non-squares: How to find the roots of numbers that are NOT square
- Square roots of negatives: Do negative numbers even have square roots?
- Cube roots and beyond: Cube roots, fourth roots, fifth roots, and so on...
- PEMDAS: Order of operations, now with exponents!

Algebra I - Powers and Roots (Squaring a number, Raising to powers, Square roots):

Algebra I – Powers and Roots (Roots of non-squares, Square roots of negatives, Cube roots and beyond, PEMDAS):