logo for solving-math-problems.com
leftimage for solving-math-problems.com

5+6-(7-√(64))^2-1 step by step










































Evaluate Expression with Parentheses

   • Evaluate the following numerical expression:

           5 + 6 - (7 - √(64))² - 1

           Simplify the expression by using the operations indicated to obtain a single numerical value.

   • Show all steps

Comments for 5+6-(7-√(64))^2-1 step by step

Click here to add your own comments

Sep 09, 2012
Evaluate Expression
by: Staff


Answer:


Part I


5 + 6 - (7 - √(64))² - 1

To simplify this expression, follow the steps indicated in the PEMDAS order of operations.

PEMDAS order tells you what to do first, second, . . . etc.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction. These steps must be evaluated in order.

Step 1: evaluate PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

There is one set of parentheses to evaluate.

(If there were nested parentheses, you would evaluate the expression inside the inner parentheses first, and then evaluate the expression within the outer parentheses.)

For this problem, the expression which must be evaluated first is shown in blue:

5 + 6 - (7 - √(64))² - 1

Follow the entire PEMDAS sequence inside the parentheses. Ignore the other parts of the expression for now.

Step 2: evaluate EXPONENTS (within parentheses)

PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

5 + 6 - (7 - √(64))² - 1

The square root is actually a fractional exponent.

The expression (7 - √(64)) can be rewritten as follows:

(7 - (64)½)

However, the only thing to be done now (according to the PEMDAS order of operations) is to evaluate the exponent:

(64)½

= 8

The expression inside the parentheses now looks like this:

(7 - 8)


Step 3: MULTIPLICATION (within parentheses)

Remember, the only thing we are evaluating at this time is the expression within the parentheses using the PEMDAS order of operations.

PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

There is no multiplication to be completed within the parentheses.


Step 4: DIVISION (within parentheses)

We are only concerned with the expression inside the parentheses.

PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction

There are no parts of the expression inside the parentheses which require division.

----------------------------------

Sep 09, 2012
Evaluate Expression
by: Staff


----------------------------------

Part II

Step 5: evaluate ADDITION & SUBTRACTION (within parentheses)

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

There is one subtraction within the parentheses.

(7 - 8)

= -1

We have completed the evaluation of the expression inside the parentheses.


The complete expression now looks like this:

5 + 6 - (-1)² - 1

There are no addition parentheses to evaluation. We will now return to Step 2: evaluate EXPONENTS as it applies to the entire expression.

Step 2: evaluate EXPONENTS (for the complete expression)

PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

5 + 6 - (-1)² - 1

(-1)²

= 1


The complete expression now looks like this:

5 + 6 - 1 - 1


Step 3: MULTIPLICATION (for the complete expression)


PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

There is no multiplication to be completed.


Step 4: DIVISION (for the complete expression)

PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction

There are no parts of your expression which require division.



Step 5: evaluate ADDITION & SUBTRACTION (for the complete expression)

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

There are operations which do require addition or subtraction.

5 + 6 - 1 - 1

= 11 - 2

= 9


You are finished. There are no further steps which need to be completed.

The final answer:

5 + 6 - (7 - √(64))² - 1 = 9


The complete step by step process of simplification looks like this:

5 + 6 - (7 - √(64))² - 1

= 5 + 6 - (7 - (64)½)² - 1

= 5 + 6 - (7 - 8)² - 1

= 5 + 6 - (-1)² - 1

= 5 + 6 - 1 - 1

= 11 - 2

= 9



Thanks for writing.

Staff
www.solving-math-problems.com



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com