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Which of these are truths, and which of these are lies? Why?

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1，2 are true and 3 is lie

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1. √(x-5) = (x-5)1/2

≠ √(x)-√(5)

Thus, the given proposition is false.

2. √(x/7) = (x/7)1/2 = (x1/2)/(71/2)
Thus, the given proposition is true.
3. √(x²+3²) = (x²+3²)1/2
To eliminate square root, the radicands should be a perfect square.
However, (x²+3²)  is not a perfect square.
Thus, the given proposition is false.

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1 Lie
2 True
3 Lie

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2-truth
3-lies

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1. Lie
2. Truth
3. Lie

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lie
truth
lie

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1.lie
2.true
3. lie

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1 is lie √（9-5）=2， √9-√5=0.76； 2 is true；3 is lie √2^2+3^2=3.61, 2+3=5

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1.Lie
2.Truth
3.Lie

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Luffy false true false

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1.True
2.True
3.Lie

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1.false 2.true 3. false

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1. Truth
2. Truth
3. lie

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1 lie, 2 true, 3 lie

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The first one is lie. It can be proven through an example. When x=16, √x-5= √16-5=√11, however, √16-√5=4-√5 which is not equal to √11.
The second one is true. √x/7 = √x*√1/7=√x/√7
The third one is a lie. for example, √4²+3²=√16+9=√25=5, but 4+3=7, doesn't match.

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1. lie.
2. True.
3. Lie.

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1. lie
2. true
3. lie

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Lies:1 and 3
Truths:2
we can use

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1.Lie
2.Truth
3.Lie

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1. Lie
2. True
3. Lie

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1 3 are lies
2 is true
can put a number to check
or square both sides

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1. Lie: √(9-4)≠3-2
2. True: √(9/4)=3/2
3. Lie: √(3^2+2^2)≠3+2

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2 is correct while 1&3 is not true
statement 1&3 is not true because the root is the whole one and we do not know x is positive or negative.