I have a few more questions that I'm not understanding. Its multiple choice however I would appreciate a breakdown on how to solve.
1.Evaluate without a calculator, using the order of operations. -2^2+20-|8-20|-squareroot of 64
a. -36
b. 4
c. 28
d. -4
2.Simplify the expression. Square root of -16
a. 4
b. -4
c. -8
d. Not a real number
-2^2+20-|8-20|-squareroot of 64
= -4 + 20 - 12 - 8
= -4
√-16 ----> not a real number
( in your first one, notice the difference between
-2^2 and (-2)^2 )
-2^2+20-|8-20|-√64
-4+20-|-12|-8
-4+20-12-8
-4
(D)
since x^2 >= 0 for all real x,
(D)
√-16 = 4i, a complex number
Sure, I can help you with these questions. Let's break down each question step-by-step.
1. Evaluate the expression without a calculator using the order of operations: -2^2 + 20 - |8 - 20| - square root of 64.
To solve this expression, we use the order of operations, which is commonly known as PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, let's tackle the exponent: -2^2. According to the rule of exponents, we should square the number first, and then apply the negative sign. So, -2^2 becomes -4.
Next, we have 20 - |8 - 20|. Inside the absolute value, we subtract 8 from 20, resulting in 12. Now, we have 20 - |12|. Applying the absolute value, we get 20 - 12, which is 8.
Continuing, we have -4 + 8 - square root of 64. The square root of 64 is 8. Therefore, the expression becomes -4 + 8 - 8.
Finally, we can combine the terms: -4 + 8 - 8 = -4.
Hence, the answer is (d) -4.
2. Simplify the expression: Square root of -16.
To simplify this expression, we need to determine if the square root of -16 is a real number or not. The square root of a negative number is not a real number but rather an imaginary number. Imaginary numbers are represented by the letter "i".
The square root of -1 is defined as "i". Therefore, we can simplify the square root of -16 as the square root of -1 times the square root of 16, which is equal to "i" times 4.
Hence, the answer is (b) -4, as "i" times 4 is -4i.