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Flashcards · Maths · Further Algebra

Surds

16 cards

  1. What is a surd?

    A root that cannot be written as a whole number or fraction, such as \(\sqrt{2}\).

  2. Why are surds left as roots?

    Their decimals never end, so the root is the exact value.

  3. What is \(\sqrt{a} \times \sqrt{a}\)?

    \(a\).

  4. What is the product rule for surds?

    \(\sqrt{a} \times \sqrt{b} = \sqrt{ab}\).

  5. Simplify \(\sqrt{12}\).

    \(2\sqrt{3}\).

  6. Simplify \(\sqrt{50}\).

    \(5\sqrt{2}\).

  7. Simplify \(\sqrt{72}\).

    \(6\sqrt{2}\).

  8. Which square numbers are useful for simplifying surds?

    4, 9, 16, 25, 36 and 49.

  9. What is \(3\sqrt{2} + 5\sqrt{2}\)?

    \(8\sqrt{2}\).

  10. Can \(\sqrt{2} + \sqrt{3}\) be simplified?

    No, because they are not like surds.

  11. What is \(\sqrt{2} \times \sqrt{8}\)?

    4.

  12. What does rationalising the denominator mean?

    Rewriting a fraction so that there is no surd on the bottom.

  13. Rationalise \(\dfrac{6}{\sqrt{3}}\).

    \(2\sqrt{3}\).

  14. What is the conjugate of \(2 + \sqrt{3}\)?

    \(2 - \sqrt{3}\).

  15. What is \((2 + \sqrt{3})(2 - \sqrt{3})\)?

    1.

  16. Expand \((2 + \sqrt{5})^2\).

    \(9 + 4\sqrt{5}\).