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Chapter 8: Problem 3

Simplify. $$1 \sqrt{w}+1 \sqrt{w}$$

Short Answer

Expert verified
2鈭归

Step by step solution

01

Understand the problem

The given expression is the addition of two terms involving square roots: 1鈭歸 + 1鈭歸.
02

Identify like terms

Notice that both terms are like terms because they both include the square root of w.
03

Add coefficients of like terms

When adding like terms, one can simply add their coefficients. The coefficient in each term is 1.
04

Combine the like terms

Add the coefficients: 1 + 1 = 2. Keep the square root: 鈭歸. Thus, 1鈭歸 + 1鈭歸 becomes 2鈭归.

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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 mathematical expressions that represent a number, which when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9. The symbol for square root is \( \sqrt{} \). In our exercise, we deal with the square root of \( w \). Always remember:
  • The square root of a number is always positive.
  • The square root of 0 is 0.
  • Square roots can be simplified by finding perfect square factors.
    • Understanding how to manipulate and combine square roots is crucial in simplifying expressions like the given example.
Like Terms
Like terms are terms that have the same variables raised to the same powers. For example, \( 3x^2 \) and \( 5x^2 \) are like terms because they both contain \( x^2 \). In our given problem, we have \( 1 \sqrt{w} + 1 \sqrt{w} \). Both terms contain \( \sqrt{w} \), making them like terms. When combining like terms, you only add or subtract the coefficients while keeping the variable part the same. This simplifies the process and makes the expression easier to manage.
Coefficients
Coefficients are the numerical parts of terms that contain variables. In the expression \( 3x \), 3 is the coefficient. In our problem, we have coefficients of 1 in both terms: \( 1 \sqrt{w} + 1 \sqrt{w} \). When dealing with like terms, we add their coefficients while keeping the variable part unchanged. This means:
  • Identify coefficients.
  • Add or subtract only the coefficients.
  • Combine the result with the variable part.
Thus, for \( 1 \sqrt{w} + 1 \sqrt{w} \), we add the coefficients (1 + 1) to get 2, giving us \( 2 \sqrt{w} \).

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