Problem 83 Evaluate each expression for \(a... [FREE SOLUTION]

Chapter 0: Problem 83

Evaluate each expression for $a=-3, b=64,$ and $c=6 .$ $$ 3 a+\sqrt{b} $$

Short Answer

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Step by step solution

Identify the Variables

Identify the values of the variables from the given problem statement. Here, they are: $a = -3$, $b = 64$, and $c = 6$.

Substitute the Values

Substitute the given values of $a$ and $b$ into the expression. So, substitute $a = -3$ and $b = 64$ into $3a + \sqrt{b}$.

Calculate the First Term

Calculate the first term by multiplying the constant 3 with $a = -3$. This gives: $3 \times (-3) = -9$.

Calculate the Second Term

Calculate the second term by taking the square root of $b = 64$. The square root of 64 is: $\sqrt{64} = 8$.

Combine the Results

Combine the results of the two terms: $-9 + 8$.

Simplify the Expression

Simplify the combined result to get the final value: $-9 + 8 = -1$.

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Key Concepts

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

substitution method

The substitution method involves replacing variables in an algebraic expression with their actual values. This is crucial for evaluating expressions accurately.
For example, in the exercise problem, the variables are provided: $a = -3$, $b = 64$, and $c = 6$. We need to substitute these values into the given expression $3a + \sqrt{b}$.
When substituting $a = -3$ and $b = 64$, the expression becomes $3(-3) + \sqrt{64}$.
This is how we translate the abstract problem into a concrete one that we can solve in the following steps.

square roots

A square root is a number that produces a specified quantity when multiplied by itself. For instance, the square root of 64 is 8, because 8 multiplied by 8 equals 64 (8^2 = 64).
Calculating the square root is a straightforward process;
when you see the square root symbol ($\sqrt{}$), you need to find the number which, when squared, equals the given value.
In our problem, after substituting the values into $3a + \sqrt{b}$, we calculate the square root of 64:
$\sqrt{64} = 8$. Knowing how to deal with square roots is essential for evaluating similar algebraic expressions.

simplifying expressions

Simplifying expressions is about combining like terms and performing arithmetic operations to turn an expression into a more manageable form.
In the final steps of our problem, simplify the combined terms: $-9 + 8$. This involves straightforward arithmetic where we combine the terms to get the final result:
$-9 + 8 = -1$.
Simplifying expressions helps in understanding the relationship between the components and solving the expressions accurately.

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91影视

Evaluate each expression for \(a=-3, b=64,\) and \(c=6 .\) $$ 3 a+\sqrt{b} $$

Short Answer

Step by step solution

Identify the Variables

Substitute the Values

Calculate the First Term

Calculate the Second Term

Combine the Results

Simplify the Expression

Key Concepts

substitution method

square roots

simplifying expressions

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