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27 Aug 2025, 21:42
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Hello!
We see many learners on our GMAT portal mixing up x = √4 with the equation x^2 = 4. A quick clarification:
Key ideas
1. x = √4 is a linear equation. A linear equation has one solution, so x = 2.
2. The radical symbol √a denotes the principal (nonnegative) square root. For any a ≥ 0, √a ≥ 0. Therefore √4 = 2, not −2.
Two different equations
(1) x = √4
Since √4 = 2, this has a single solution: x = 2.
(2) x^2 = 4
Taking square roots of both sides gives x = ±√4, so the two solutions are x = 2 and x = −2.
Why √4 is not ±2
√4 is a single number by definition: the principal, nonnegative root. Allowing −2 would contradict that definition.
Remember
√a gives the nonnegative root.
Solving x^2 = a (with a ≥ 0) yields two solutions: x = ±√a.
Mini-check
Solution to x = √9 gives x = 3, while the solutions to x^2 = 9 are x = ±3.
Hope this helps.
Thanks.
Experts' Global
We see many learners on our GMAT portal mixing up x = √4 with the equation x^2 = 4. A quick clarification:
Key ideas
1. x = √4 is a linear equation. A linear equation has one solution, so x = 2.
2. The radical symbol √a denotes the principal (nonnegative) square root. For any a ≥ 0, √a ≥ 0. Therefore √4 = 2, not −2.
Two different equations
(1) x = √4
Since √4 = 2, this has a single solution: x = 2.
(2) x^2 = 4
Taking square roots of both sides gives x = ±√4, so the two solutions are x = 2 and x = −2.
Why √4 is not ±2
√4 is a single number by definition: the principal, nonnegative root. Allowing −2 would contradict that definition.
Remember
√a gives the nonnegative root.
Solving x^2 = a (with a ≥ 0) yields two solutions: x = ±√a.
Mini-check
Solution to x = √9 gives x = 3, while the solutions to x^2 = 9 are x = ±3.
Hope this helps.
Thanks.
Experts' Global
