Evaluate √81 – | -8 + 17 | + 3

An algebraic expression is an expression that helps to express numbers using alphabets without specifying their actual values. The letters that are used to hide the actual values are known as variables. 

Constants are actually numbers in the expression. An expression can consist of variables and constants or only variables or only constants. When a variable is multiplied by a constant it is known as a coefficient. 

The algebraic expression consists of operators like addition, subtraction, division, multiplication, and many more. The algebraic expressions are always commutative, associative, and distributive.

e.g. 

Given that: 4y – 5.

Here:

• y is the variable, 
• 4 and 5 are constants. 
• 4y is the coefficient. 

Types of Algebraic expressions

1. Monomial Expression: An expression that has only one term. Example: 3x, x, 4a.
2. Binomial Expression: An expression that has two terms. Example: 4x + 7 has two terms 4x and 7.
3. Polynomial Expression: An expression with more than two terms is a polynomial expression. Example: ax+b+cy has three terms.
4. Numeric Expression: An expression that has only constants but no variables. Example: 15/2,3+6
5. Variables Expression: An expression that comprises variables and constants. Example: 5y + 33

Absolute Value

The absolute value is always positive irrespective of the sign of the complex number. It is just a magnitude. It is often known by the name of modulus and is often represented by | x | where x is any value. The absolute value of any number is always the positive and the absolute value of a negative number is also positive.

For example find absolute value of -6-8

As we know: -6-8 = – 14

| -14 | = 14

Formulas

Some formulas for algebraic expression:

• |-a| = |a| = a
• √(a+b) ² = ±(a+b) 
• √(a-b) ² = ±(a-b) 

Evaluate: √81 – | -8 +17 |  + 3

Solution:

The √81 has two values +9 or -9

| -8 +17 | =| 9 | = 9

Case 1: when we consider the positive square root that is +9

9 – 9 + 3 = 3

Case 2: When we consider the negative square root that is -9

-9 – 9 + 3 = -15

So there are two answers of the numerical expression 3 and -15

Similar Problems

Problem 1: Find the value of ∛{( 64 ) +33 + | √81|}.

Solution: 

∛{64} = 4

√81 = ± 9

| ±9 | = 9

So evaluating the expression we get

4 + 9 + 33 = 46

Problem 2: Evaluate the expression using x=1, y=0 ; 4y+ x +2xy+1.

Solution: 

Putting the values of x and y in the expression as,

4y + x +2xy+1 

we get 

4(0) + 1 + 2(0)(1) +1 = 2

Problem 3: Evaluate √(64) +| -7 – 17 |

Solution:

√64 = ±8

|-7-17|= |-24|= 24

Case 1: When +8 is considered

8 + 24 = 32

Case 2: When -8 is considered

-8 + 24 = 16

The answers are 16 and 32.

Problem 4: Find | -6 × 5 + 7| + 3.

Solution: 

We evaluate the modulus first

| -30 + 7| = | -23 | = 23

23 + 3 = 26