Problem 67 Simplify each expression. $$ ... [FREE SOLUTION]

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Chapter 0: Problem 67

Simplify each expression. $$ -7(\sqrt{36})-(-2)(-3) $$

Short Answer

Expert verified

-48

Step by step solution

Simplify the Square Root

First, simplify the square root in the expression. \ \ $ \sqrt{36} = 6 $

Substitute Simplified Value

Next, substitute the simplified value back into the expression: \ \ $ -7(\sqrt{36}) - (-2)(-3) $ becomes \ $ -7(6) - (-2)(-3) $

Multiply

Now, perform the multiplication in the expression: \ \ $ -7 \times 6 = -42 $ and $ -2 \times -3 = 6 $. \ \ So the expression becomes \ $ -42 - 6 $

Subtract

Lastly, perform the subtraction: \ \ $ -42 - 6 = -48 $

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Key Concepts

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

Square Roots

Square roots are a fundamental concept in mathematics. A square root of a number is a value that, when multiplied by itself, gives the original number. For instance, in this exercise, we had to find the square root of 36. The square root of 36 is 6 since 6 multiplied by 6 equals 36. Generally, the square root symbol is represented as $ \sqrt{} $. Understanding square roots helps in simplifying expressions and solving many types of mathematical problems. When simplifying expressions, always look to simplify the square roots first. This makes the subsequent steps much easier.

Multiplication

Multiplication is one of the basic arithmetic operations. It is the process of calculating the total of one number added repeatedly a specified number of times. In our exercise, after simplifying the square root, we proceed to multiply. We have two multiplication operations: $ -7 \times 6 = -42 $ and $ -2 \times -3 = 6 $. Remember, when multiplying two negative numbers, the result is positive, which is why $ -2 \times -3 $ equals 6. Mastering multiplication is crucial for simplifying expressions and solving more complex mathematical problems. Pay close attention to the signs of the numbers you are multiplying, as they affect the result.

Subtraction

Subtraction is another fundamental arithmetic operation. It involves taking one number away from another. In our exercise, after performing the multiplications, we need to subtract the results: $ -42 - 6 $. Subtraction of a positive number from a negative number results in a larger negative number, hence $ -42 - 6 = -48 $. Understanding how to subtract correctly, especially when dealing with negative numbers, is essential for obtaining correct results in mathematical expressions.

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91影视

Simplify each expression. $$ -7(\sqrt{36})-(-2)(-3) $$

Short Answer

Step by step solution

Simplify the Square Root

Substitute Simplified Value

Multiply

Subtract

Key Concepts

Square Roots

Multiplication

Subtraction

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