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Showing 1 question for Class 9. Tap a card to reveal the answer.

MathematicsNumber Systemsmedium

Rationalise the denominator of 1 / sqrt(2).

Reveal answer ↓

What it is

Rationalising clears a surd (root) from the denominator by multiplying top and bottom by it.

Answer

Multiply the numerator and denominator by sqrt(2): (1/sqrt(2)) x (sqrt(2)/sqrt(2)) = sqrt(2) / 2. So 1/sqrt(2) = sqrt(2)/2, which is about 0.707. Rationalising removes the irrational number (surd) from the denominator.

1/sqrt(a) = sqrt(a)/a

  • •Multiply top and bottom by sqrt(2)
  • •= sqrt(2)/2
  • •Removes the surd from the denominator

Why learn this

It makes fractions easier to compute and compare - important in exams and in engineering maths.

💡 Memory trick

Multiply top and bottom by the same surd - the root moves upstairs.