Telangana TET Paper 1 Exam Model Paper 3

Section: Mathematics

Question : 101 of 150

Marks: +1, -0

Simplify :

\frac{2}{1-\sqrt2}

Solution:

Concept:

Rationalize the denominator by multiplying numerator and denominator by the conjugate of the denominator.

Explanation:

Start with

\frac{2}{1-\sqrt{2}}

Multiply numerator and denominator by the conjugate

(1+\sqrt{2})

\frac{2 \times (1+\sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}

Denominator simplifies:

(1)^2 - (\sqrt{2})^2 = 1 - 2 = -1

Numerator:

2 + 2\sqrt{2}

\frac{2+2\sqrt{2}}{-1} = -(2+2\sqrt{2}) = -2(1+\sqrt{2})

Answer:

-2(1+\sqrt{2})

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