It is standard to remove surds from the bottom of a fraction.
Multiply top and bottom by the surd.
Example: 1/√2 = (1×√2)/(√2×√2) = √2/2
Example: 5/√3 = 5√3/3
Multiply top and bottom by the conjugate. The conjugate of a+√b is a-√b.
Example: 1/(2+√3) × (2-√3)/(2-√3) = (2-√3)/(4-3) = 2-√3
We use (a+b)(a-b) = a2 - b2 to remove the surd.
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Rationalise and simplify:1/√53/√2√6/√31/(3+√2)4/(5-√3)(√5+1)/(√5-1)
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