Surds & Indices

LSSSSB Non-Technical · Mathematics · 12 practice questions with answers and explanations: 3 Easy, 9 Medium, 0 Hard.

Sample questions

Sample Easy question 1

Find the value of (3²)³.

  1. 81
  2. 729
  3. 243
  4. 59049
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Answer: B. (3²)³ = 3⁶ = 729.

Sample Easy question 2

Find the value of (√5 + √3)(√5 − √3).

  1. 8
  2. √15
  3. 4
  4. 2
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Answer: D. (a + b)(a − b) = a² − b² = 5 − 3 = 2.

Sample Easy question 3

Find the value of 2⁵ × 2³ ÷ 2⁴.

  1. 64
  2. 32
  3. 16
  4. 8
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Answer: C. Add and subtract the powers: 2^(5+3−4) = 2⁴ = 16.

Sample Medium question 4

Find the value of 16^(1/4) × 8^(2/3).

  1. 4
  2. 16
  3. 6
  4. 8
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Answer: D. 16^(1/4) = 2 and 8^(2/3) = 4, so the product is 8.

Sample Medium question 5

Rationalise the denominator of 1/(√3 − √2).

  1. 1/(√3 + √2)
  2. √3 − √2
  3. √6
  4. √3 + √2
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Answer: D. Multiply by (√3 + √2)/(√3 + √2): the denominator becomes 3 − 2 = 1, giving √3 + √2.

Sample Medium question 6

If 2^(x−1) + 2^(x+1) = 320, find x.

  1. 6
  2. 7
  3. 5
  4. 8
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Answer: B. 2^x(1/2 + 2) = 320 → 2^x × 2.5 = 320 → 2^x = 128 = 2⁷, so x = 7.

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