Is the following statement true or false?
If and , then

Ask by Grant Edwards. in the United States

Mar 31,2025

Question

Is the following statement true or false? If $$ x^{2}=p $$ and $$ p>0 $$, then $$ x=\sqrt{p} $$

UpStudy AI · Accepted Answer

Given that $$ x^2 = p $$ and $$ p > 0 $$, the equation has two solutions:

1. $$ x = \sqrt{p} $$
2. $$ x = -\sqrt{p} $$

The notation $$ \sqrt{p} $$ denotes the principal (non-negative) square root. Since the equation $$ x^2 = p $$ also has the solution $$ x = -\sqrt{p} $$, the statement "if $$ x^2 = p $$ and $$ p>0 $$, then $$ x=\sqrt{p} $$" is false.
The statement is false because $$ x $$ can also be $$ -\sqrt{p} $$.

Is the following statement true or false?
If and , then

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Is the following statement true or false? If and , then