Problem 88 - Elementary Algebra

Question

For exercises 85-88, use a calculator to evaluate. If the calculator has parentheses, use them. $$ 3+(8-1)^{2} $$

Step-by-Step Solution

Answer

The answer is 52.

Step 1 - Identify the Expression Inside the Parentheses

First, identify the expression inside the parentheses: The expression is \((8-1)\).

Step 2 - Evaluate the Parentheses

Next, evaluate the expression inside the parentheses: \(8 - 1 = 7\).

Step 3 - Square the Result

Now, take the result from the parentheses and square it: \((7)^2 = 49\).

Step 4 - Add to the Remaining Number

Finally, add the result to the remaining number: \(3 + 49 = 52\).

Key Concepts

Parentheses in Math

Parentheses are essential in math because they tell you which operations to perform first. Without parentheses, you might do calculations in the wrong order and get an incorrect result.

For example, look at the expression. Here it is: \( 3+(8-1)^2 \).

Notice the parentheses around \(8-1\). This indicates we need to calculate \(8-1\) first.

Parentheses act like instructions that guide you through solving the problem correctly.

Evaluating Expressions

Evaluating an expression means finding its value. Let's use our example: \( 3+(8-1)^2 \).

Follow these steps to evaluate it:

• Spot any parentheses: In our example, we have \( (8-1) \).
• Calculate inside the parentheses: \( 8-1=7 \).
• Handle any exponents: Square the \( 7 \), so \( 7^2=49 \).
• Wrap it up: Add the result to the remaining number: \( 3+49=52 \).

Break down expressions into smaller parts, then solve each part step by step. This makes complicated problems easier to handle.

Squaring Numbers

Squaring a number means multiplying it by itself. For example, squaring 7 is written as \(7^2\).

Let's see why: \(7^2=7 \times 7=49\).

When you square numbers, their value grows quickly. Squaring is a key math skill.

Review these examples:

• \(2^2=4\)
• \(3^2=9\)
• \(4^2=16\)

Knowing how to square numbers will help you with many math problems. It’s like adding power to your calculating toolkit!