Order of Operations: Roots - Examples, Exercises and Solutions

Understanding Order of Operations: Roots

Complete explanation with examples

As we have learned in previous lessons, when working with combined operations the order of the basic operations must be followed in order to get the correct result. However, before performing these the parentheses and then the roots and powers must first be solved.

Roots are very important in mathematical calculations. They are present in a variety of exercises ranging from algebraic problems for solving a second degree equation using the general formula, to geometric problems like determining the length of the hypotenuse of a right-angled triangle. Therefore, it is fundamental that we learn how to solve combined operations where this operation appears.

When we have simplified the root and power operations, we can continue solving the exercise according to the order of the basic operations: multiplications and divisions first, followed by additions and subtractions.

Let's revisit the order of the operations:

  1. Parentheses
  2. Powers and roots
  3. Multiplication and division
  4. Addition and subtraction
Detailed explanation of the BODMAS/PEMDAS rule highlighting 'Order' (Exponents) with symbols like √x and x², crucial for solving complex arithmetic expressions step by step.

Detailed explanation

Practice Order of Operations: Roots

Test your knowledge with 24 quizzes

\( 10:2-2^2= \)

Examples with solutions for Order of Operations: Roots

Step-by-step solutions included
Exercise #1

2033:3= 20-3^3:3=

Step-by-Step Solution

First, compute the power: 33=27 3^3 = 27 .

Next, divide: 27÷3=9 27 \div 3 = 9 .

Finally, subtract: 209=11 20 - 9 = 11 .

Answer:

11 11

Exercise #2

1542:2= 15-4^2:2=

Step-by-Step Solution

First, compute the power: 42=16 4^2 = 16 .

Next, divide: 16÷2=8 16 \div 2 = 8 .

Finally, subtract: 158=7 15 - 8 = 7 .

Answer:

7 7

Exercise #3

1052:5= 10-5^2:5=

Step-by-Step Solution

First, compute the power: 52=25 5^2 = 25 .

Next, divide: 25÷5=5 25 \div 5 = 5 .

Finally, subtract: 105=5 10 - 5 = 5 .

Answer:

5 5

Exercise #4

816×3= 8 - \sqrt{16} \times 3 =

Step-by-Step Solution

First, evaluate the square root: 16=4\sqrt{16}=4.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Multiplication: 4×3=124 \times 3 = 12

2. Subtraction: 812=48 - 12 = -4

So, the correct answer is 4 -4 .

Answer:

4 -4

Exercise #5

7+495= 7 + \sqrt{49} - 5 =

Step-by-Step Solution

First, evaluate the square root: 49=7\sqrt{49}=7.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Addition: 7+7=147 + 7 = 14

2. Subtraction: 145=914 - 5 = 9

So, the correct answer is 9 9 .

Answer:

9 9

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