Practice Problems (Junior Cert Mathematics): Flashcards

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Factor type that helps simplify surds

Perfect square

Simplified form of 50\sqrt{50}

525\sqrt{2}

Simplified form of 18\sqrt{18}

323\sqrt{2}

Simplified form of 8\sqrt{8}

222\sqrt{2}

How to add surds like 32+223\sqrt{2} + 2\sqrt{2}

Add coefficients: (3+2)2=52(3+2)\sqrt{2} = 5\sqrt{2}

18+8\sqrt{18} + \sqrt{8} simplified

525\sqrt{2}

First step: multiply 3×12\sqrt{3} \times \sqrt{12}

Multiply inside: 3×12=36\sqrt{3 \times 12} = \sqrt{36}

3×12\sqrt{3} \times \sqrt{12} simplified

66

First step: divide 753\frac{\sqrt{75}}{\sqrt{3}}

Divide inside: 753=25\sqrt{\frac{75}{3}} = \sqrt{25}

753\frac{\sqrt{75}}{\sqrt{3}} simplified

55

5050 as product with perfect square factor

25×225 \times 2

50+188\sqrt{50} + \sqrt{18} - \sqrt{8} simplified

626\sqrt{2}

Why 2\sqrt{2} stays as is

22 is not a perfect square

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