A surd is a root that will not simplify to a whole number, like 2 or3. They look intimidating but follow simple rules — and many “algebra” fractions hide a cube identity that makes the whole thing cancel.
Surd moves & the cube-fraction trick
• Simplify: pull out the largest perfect square — 98=49×2=72. You can only add or subtract like surds (same number under the root).
• Rationalise: to clear roots from a−b1, multiply top and bottom by the conjugate a+b; the bottom becomes a−b with no surd left.
• Cube-fraction cancelling: a denominator like a2+ab+b2 is the partner of a3−b3, so a2+ab+b2a3−b3=a−b. Spot the cubes (e.g. 8x3=(2x)3) and cancel.
Keep these values memorised: 2≈1.41,3≈1.73,5≈2.24.
2 question types · 8 solved examples from real SSC papers
Surds shrink fast once you factor out perfect squares and rationalise with the conjugate. Cubic-over-quadratic fractions collapse via the a3−b3 identity.
How to solve this type
Simplify by factoring out the largest perfect square: 98=49×2=72. Add only LIKE surds (same number under the root). To rationalise a−b1, multiply top and bottom by the conjugate a+b so the bottom becomes a−b. Keep 2≈1.41,3≈1.73,5≈2.24 handy.
