Prove that 5 + √2 is irrational
CLASS 10TH CBSE SAMPLE PAPER 2018-19
MATHEMATICS
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Suppose 5 +3√3 is rational .
Let 5 +3√3 = r where r is a rational.
∴ (5 +3√3)² = r²
∴ 25+27 +30√3 = r²
∴√3 = (r² - 52) / 30
Now , LHS = √3 is an irrational number .
RHS (r² - 7) / 2 is a rational number .
But rational number cannot be equal to an irrational.
∴our supposition is wrong.
∴ 5 + 3√3 is irrational .
Let 5 +3√3 = r where r is a rational.
∴ (5 +3√3)² = r²
∴ 25+27 +30√3 = r²
∴√3 = (r² - 52) / 30
Now , LHS = √3 is an irrational number .
RHS (r² - 7) / 2 is a rational number .
But rational number cannot be equal to an irrational.
∴our supposition is wrong.
∴ 5 + 3√3 is irrational .
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