Evaluate: 3^2 + 2^2 x 5 - sqrt 25 over 8 - 4 / 2 + 2
I am confused on the order in which I solve this. Please help!
ORDER OF OPERATIONS:
P.E.M.D.A.S.
Parenthesis Exponents Multiplication Division Addition Subtraction
Mnemonic:
"Please Excuse My Dear Aunt Sally"
Roots are considered exponents.
Example: x^(1/2) = sqrt(x)
To solve this expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
Let's break down the expression step by step:
1. Exponents:
Evaluate each exponent in the expression:
3^2 = 9
2^2 = 4
The expression becomes:
9 + 4 x 5 - sqrt(25) / 8 - 4 / 2 + 2
2. Square Root:
Evaluate the square root of 25:
sqrt(25) = 5
The expression becomes:
9 + 4 x 5 - 5 / 8 - 4 / 2 + 2
3. Multiplication and Division:
Perform any multiplication or division operations from left to right.
4 x 5 = 20
5 / 8 = 0.625
4 / 2 = 2
The expression becomes:
9 + 20 - 0.625 - 2 + 2
4. Addition and Subtraction:
Perform any addition or subtraction operations from left to right.
9 + 20 = 29
29 - 0.625 = 28.375
28.375 - 2 = 26.375
26.375 + 2 = 28.375
So, the result of the expression is 28.375.