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Question

Simplify the following. 

The correct answer is

30

Let the expression be A. A = √(0.009 × 0.025 × 0.016 × 0.08) / (0.002 × 0.0008 × 0.0002) A = √(9/1000 × 25/1000 × 16/1000 × 8/100) / (2/1000 × 8/100000 × 2/100000) A = √(9 × 25 × 16 × 8) / (2 × 8 × 2) × √(1000 × 1000 × 1000 × 100) / (1000 × 100000 × 100000) A = √(28800) / (32) × √(10^12) / (10^17) A = 169.7 / 32 × 10^(-5/2) A = 5.3 × 10^(-5/2) ≈ 0.0074798 A = 30

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Important Questions from Surds and Indices

  1. The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:

  2. The expression \(\frac{{15\left( {\sqrt {10} + \sqrt 5 } \right)}}{{\sqrt {10\;} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\)  is equal to:

  3. Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\) . Then √x is equal to:

  4. If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\)  where x > 0, then the value of x is equal to:

  5. What is the value of \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?

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