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Worked solution

Rationalise a surd denominator

Simplify 235−2−2\dfrac{23}{5-\sqrt2}-\sqrt2.

CJC · Discussion · Question 7

Answer

55.

Multiply by the conjugate

235−2−2=23(5+2)(5−2)(5+2)−2=23(5+2)25−2−2=5\dfrac{23}{5-\sqrt2}-\sqrt2=\dfrac{23(5+\sqrt2)}{(5-\sqrt2)(5+\sqrt2)}-\sqrt2=\dfrac{23(5+\sqrt2)}{25-2}-\sqrt2=5.

How did this part go?

Common mistakes

The denominator becomes 25 − 2, not 25 + 2.

Read the hint