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10 grade maths

How do you solve w² = 4 where w is a real number?

Profile image of Aniket Singh
10 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer10 Months ago

To solve the equation \( w^2 = 4 \), we need to find the values of \( w \) that satisfy this equation.

Steps to Solve

1. **Take the square root of both sides**: Since we are dealing with a square, we can apply the square root to both sides of the equation.

2. **Consider both positive and negative roots**: The square root of 4 can be both positive and negative. Thus, we write:

  • \( w = \sqrt{4} \) which gives \( w = 2 \)
  • \( w = -\sqrt{4} \) which gives \( w = -2 \)

Final Solutions

The solutions to the equation \( w^2 = 4 \) are:

  • \( w = 2 \)
  • \( w = -2 \)

Both values are real numbers, and they satisfy the original equation. Thus, the complete solution set is \( w = 2 \) and \( w = -2 \).

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