For example, here's an expression: $\sqrt{x^2 + x^2}$. Will it be equal to $\sqrt{2x^2}$?
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1Yes, of course. – JMoravitz Sep 01 '20 at 17:09
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1When $a=b$ you can replace $a$ by $b$ everywhere. – TheSilverDoe Sep 01 '20 at 17:10
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1To emphasize, the summands need to be under the same square root. $\sqrt{x}+\sqrt{x}$ is not the same as $\sqrt{2x}$. That said, this should have been covered by the "B" in BEDMAS or whatever order of operations mnemonic you learned. – JMoravitz Sep 01 '20 at 17:15
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@JMoravitz thank you – JustLearn Sep 01 '20 at 19:31
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Yes. $$\sqrt{x^2+x^2}\equiv \sqrt{2x^2}$$
However, be careful that $$\sqrt{x^2+\sqrt{x^2}}\neq\sqrt{2x^2}\neq\sqrt{x^2}+\sqrt{x^2}$$
Rhys Hughes
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