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SingaporeAdditional MathematicsQuick questions

Algebra: Surds, Indices and Polynomials

Quick questions on Surds and rationalising the denominator: N(A)-Level Additional Mathematics

9short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is simplifying a surd?
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To simplify, find the largest perfect-square factor of the number and take its root outside:
What is multiplying?
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Multiply the whole-number parts together and the surd parts together, then simplify:
What is rationalising a single-surd denominator?
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To clear a surd such as b\sqrt{b} from the denominator, multiply the top and bottom by that surd:
What is rationalising with a conjugate?
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When the denominator is b+cb + \sqrt{c}, multiply top and bottom by its conjugate b−cb - \sqrt{c}. The denominator becomes a difference of two squares, which removes the surd:
What is not taking the largest square factor?
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72=218\sqrt{72} = 2\sqrt{18} is not fully simplified; pull out 3636 to get 626\sqrt{2}.
What is wrong conjugate?
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The conjugate of 3+53 + \sqrt{5} is 3−53 - \sqrt{5}, changing only the sign between the terms.
What is q1?
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Simplify 45\sqrt{45}. [1 mark]
What is q2?
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Simplify 8+32\sqrt{8} + \sqrt{32}. [2 marks]
What is q3?
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Rationalise 12−3\dfrac{1}{2 - \sqrt{3}}. [3 marks]

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