Seudónimo Seudónimo
  • 19-04-2018
  • Mathematics
contestada

determine whether sqrt(a)+sqrt(a)=2a is sometimes, always, or never true

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MsEHolt MsEHolt
  • 29-04-2018
This is sometimes true; it is only true for a=1 or a=0.

We can combine radicals much as we do variables:
[tex]\sqrt{a}+\sqrt{a}=2a \\ \\2\sqrt{a}=2a[/tex]

Divide both sides by 2:
[tex]\frac{2\sqrt{a}}{2}=\frac{2a}{2} \\ \\\sqrt{a}=a[/tex]

We can cancel the square root by squaring both sides:
[tex](\sqrt{a})^2=a^2 \\ \\a=a^2[/tex]

Now we can divide by a:
[tex]\frac{a}{a}=\frac{a^2}{a} \\ \\1=a[/tex]

However, if we use a=0 this also works.
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rwilborn100p3dh9t rwilborn100p3dh9t
  • 30-04-2018
Answer: Sometimes (don't ridicule if wrong hehe :) 
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