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Chapter 0: Problem 103

Find the value of each expression if \(x=2\) and \(y=-1\) \(\sqrt{x^{2}}\)

Short Answer

Expert verified
2

Step by step solution

01

Substitute the Values

Replace the variable \(x\) with the given value, which is 2. The expression becomes \(\root{x^2}\).
02

Calculate the Exponent

Calculate the value inside the square root by raising 2 to the power of 2: \(2^2\). This gives you \(4\).
03

Simplify the Square Root

Find the square root of 4: \(\root{4}\). The result is 2.

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Key Concepts

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

evaluating expressions
Evaluating expressions simply means finding the value of an algebraic expression by substituting the given values for its variables. In our exercise, we are working with an expression that includes the variable \(x\). The given value for \(x\) is \(2\). This step requires us to replace \(x\) with \(2\) in the expression \(\root{x^2}\).

Here's a simple guide on how to evaluate expressions:
  • Identify the variables in the expression.
  • Replace the variables with their given values.
  • Follow the order of operations (PEMDAS/BODMAS) to simplify.
Remember, substituting values is the first step in evaluating any algebraic expression. It sets the stage for further calculations, such as applying exponents or finding square roots.

exponents
An exponent tells us how many times to multiply a number by itself. In our exercise, the expression contains \(x^{2}\), which means \(x\) is raised to the power of 2. Given that \(x=2\), we calculate the exponent by raising 2 to the power of 2. This can be written mathematically as \(2^2\).

Here is a quick breakdown:
  • Write the base number, in this case, \(2\).
  • Identify the power, which is \(2\) (since \(2^2\) means 2 multiplied by itself).
  • Multiply 2 by itself to get the result: \(2 \times 2 = 4.\)
Thus, \(2^2=4\). Understanding exponents is crucial for simplifying complex expressions.

square roots
The square root of a number is a value that, when multiplied by itself, gives the original number. In our exercise, we need to find the square root of \(4\), which is written as \(\root{4}\).

Steps to find the square root:
  • Identify the number under the square root symbol (here, it鈥檚 \(4\)).
  • Find a number that, when multiplied by itself, gives \(4\).
  • This number is \(2\) because \(2 \times 2 = 4.\)
Therefore, the square root of \(4\) is \(2\). Knowing how to find square roots helps simplify expressions and solve quadratic equations.

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Most popular questions from this chapter

Simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. $$ \frac{\left(4 x^{-1} y^{1 / 3}\right)^{3 / 2}}{(x y)^{3 / 2}} $$

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$\frac{1+x}{2 x^{1 / 2}}+x^{1 / 2} \quad x>0$$

Simplify each expression. Assume that all variables are positive when they appear. $$\sqrt[3]{-40 x^{14} y^{10}}$$

Simplify each expression. $$4^{3 / 2}$$

Simplify each expression. Assume that all variables are positive when they appear. $$6 \sqrt{5}-4 \sqrt{5}$$
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