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Chapter 9: Problem 108

Find the value of the expression without using a calculator. $$\frac{12-\sqrt{81}}{3}$$

Short Answer

Expert verified
The value of the given expression is 1.

Step by step solution

01

Evaluate the Square Root

First we need to deal with the square root operation. This is the 'Indices' in BIDMAS/BODMAS. The operation \(\sqrt{81}\) results in 9.
02

Perform the Subtraction

Substitute 9 (the result of \(\sqrt{81}\)) into the expression. Now our expression is \(12 - 9\) which equals to 3. This is the 'Subtraction' part of BIDMAS/BODMAS.
03

Perform the Division

Our current expression is \( \frac{3}{3}\). Divide 3 by 3 to find the final value. It results in 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Square Root Evaluation
The process of square root evaluation involves finding a number which, when multiplied by itself, gives the original number. For example, the square root of 81 is the number 9, because 9 multiplied by itself (9 脳 9) equals 81.
When tackling expressions that involve square roots, always start by evaluating the square root. In our exercise, the square root of 81 is evaluated first, simplifying the expression right from the outset.
BIDMAS/BODMAS: A Key to Order of Operations
BIDMAS/BODMAS is an acronym crucial for solving arithmetic expressions:
  • Brackets
  • I/Orders (Indices or Order for exponents/roots)
  • Division and Multiplication
  • Addition and Subtraction
The sequence is important because it guides the order in which operations should be performed. Jumping to subtraction before resolving indices could lead to incorrect answers.
In our problem, we followed BIDMAS by first handling the square root (an Index) before moving to subtraction and division.
Performing Basic Arithmetic Operations
Arithmetic operations like addition, subtraction, multiplication, and division are foundational for mathematics.
For the expression \(12 - \sqrt{81}\), after simplifying the square root, subtraction follows. Here, 12 minus 9 results in 3. Finally, division is carried out: 3 divided by 3 gives us 1.
It's vital to perform these operations in the correct order to obtain accurate results.
Expression Simplification Explained
Expression simplification refers to the process of reducing an expression to its simplest form. This involves performing all operations in the correct order and consolidating terms as much as possible.
In our example, we simplified the expression \(\frac{12-\sqrt{81}}{3}\) by evaluating the square root first, then performing subtraction and division in the correct order based on BIDMAS. The final simplified value of the expression is 1.
This ensures clarity and accuracy in mathematics tasks, helping to prevent errors.

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Most popular questions from this chapter

Solve the equation. $$6-x=\sqrt{x}$$

Find the distance between the two points. Round your answer to two decimal places, if necessary. $$(1,2),(5,5)$$

Determine whether the lines are parallel, perpendicular, or neither. $$ \begin{aligned} &y=\frac{2}{3} x-\frac{3}{5} \\ &y=\frac{2}{3} x+\frac{3}{5} \end{aligned} $$

Find the conjugate of the expression. Then find the product of the expression and its conjugate. $$\sqrt{u}-\sqrt{2}$$

Find the distance between the two points. Round your answer to two decimal places, if necessary. $$(3,-2),(4,6)$$
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