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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5Easy
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From the equation (p^2=2q^2), what do we learn about (p^2)?

Answer and explanation

Correct answer: (p^2) is even

Step 1: In (p^2=2q^2), the right side has a factor (2). Step 2: Therefore (p^2) is divisible by (2) and is even. Step 3: A number with factor (2) is even.

Related tags

Even SquareSqrt2 ProofClass 10Proof Of Irrationality Of √2√3√5Proof Of Irrationality Of 2 3 5Real NumbersMathematicsClass 10 Mcq
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10 more MCQs
  1. 1Which assumption is taken first to prove that (\sqrt{2}) is irrational?
  2. 2If (\sqrt{2}=\frac{p}{q}), what is obtained after squaring both sides?
  3. 3If (p^2) is even, which conclusion about (p) is correct?
  4. 4If (p) is even, in which form can (p) be written?
  5. 5What conclusion is obtained by putting (p=2k) in (p^2=2q^2)?
  6. 6What is the final contradiction in the proof of (\sqrt{2})?
  7. 7What is the correct final conclusion of the proof of (\sqrt{2})?
  8. 8If (\sqrt{3}) is assumed rational, in which form is it written?
  9. 9If (\sqrt{3}=\frac{p}{q}), which equation is obtained after squaring?
  10. 10From the equation (p^2=3q^2), what do we know about (p^2)?
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