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Square & Cube Roots, Surds & Indices – Free Practice Questions

Square & Cube Roots, Surds & Indices is part of Maths (Quantitative Aptitude) in government exams such as SSC MTS, SSC CHSL, SSC CGL, RRB Group D / Level-1, RRB NTPC and others. This page has 200 free practice questions in English and Hindi, with correct answers and explanations and short revision notes.

वर्गमूल, घनमूल, करणी और घातांक – हिंदी और अंग्रेज़ी में 200 निःशुल्क अभ्यास प्रश्न, उत्तर और व्याख्या के साथ।

Read short notesPractise with explanationsQuick quiz (10 questions)Timed topic test

Questions: 200 · Sets of 50: 4 · Difficulty mix: 185 easy, 15 medium · Languages: English and Hindi

Sample Square & Cube Roots, Surds & Indices questions with answers

Q1. What is the value of √144 + ∛27?

√144 + ∛27 का मान क्या है?

  1. 12
  2. 14
  3. 15
  4. 18
Answer: 15. √144 = 12 and ∛27 = 3. So 12 + 3 = 15.
√144 = 12 और ∛27 = 3। अतः 12 + 3 = 15

Q2. Find the value of (2^4)^3

(2^4)^3 का मान ज्ञात करें।

  1. 4096
  2. 2048
  3. 128
  4. 24
Answer: 4096. (a^m)^n = a^(m×n) = 2^12 = 4096.
(a^m)^n = a^(m×n) = 2^12 = 4096

Q3. Simplify: 5^6 × 5^3 ÷ 5^7

सरल करें: 5^6 × 5^3 ÷ 5^7

  1. 125
  2. 25
  3. 10
  4. 1953125
Answer: 25. Add powers when multiplying, subtract when dividing: 5^(6+3−7) = 5^2 = 25.
गुणा में घातें जोड़ें, भाग में घटाएँ: 5^(6+3−7) = 5^2 = 25

Q4. Find the value of (3^2)^2

(3^2)^2 का मान ज्ञात करें।

  1. 12
  2. 243
  3. 81
  4. 27
Answer: 81. (a^m)^n = a^(m×n) = 3^4 = 81.
(a^m)^n = a^(m×n) = 3^4 = 81

Q5. Find the cube root of 1728.

1728 का घनमूल ज्ञात करें।

  1. 11
  2. 14
  3. 12
  4. 13
Answer: 12. 12 × 12 × 12 = 1728, so ∛1728 = 12.
12 × 12 × 12 = 1728, अतः ∛1728 = 12

Q6. Find the cube root of 729.

729 का घनमूल ज्ञात करें।

  1. 8
  2. 10
  3. 11
  4. 9
Answer: 9. 9 × 9 × 9 = 729, so ∛729 = 9.
9 × 9 × 9 = 729, अतः ∛729 = 9

Q7. Find the value of 7^0 + 5^2

7^0 + 5^2 का मान ज्ञात करें।

  1. 26
  2. 33
  3. 32
  4. 25
Answer: 26. Any non-zero number to the power 0 is 1. So 1 + 5^2 = 1 + 25 = 26.
किसी भी शून्येतर संख्या की घात 0 = 1। अतः 1 + 5^2 = 1 + 25 = 26

Q8. Find the value of 8^0 + 2^3

8^0 + 2^3 का मान ज्ञात करें।

  1. 16
  2. 8
  3. 17
  4. 9
Answer: 9. Any non-zero number to the power 0 is 1. So 1 + 2^3 = 1 + 8 = 9.
किसी भी शून्येतर संख्या की घात 0 = 1। अतः 1 + 2^3 = 1 + 8 = 9

Q9. Simplify: (2^2)^5

सरल कीजिए: (2^2)^5

  1. 2^7
  2. 4^10
  3. 2^11
  4. 2^10
Answer: 2^10. (aᵐ)ⁿ = aᵐⁿ, so the power is 2 × 5 = 10. Answer: 2^10.
(aᵐ)ⁿ = aᵐⁿ, अतः घात 2 × 5 = 10। उत्तर: 2^10।

Q10. Simplify: 5^4 × 5^3

सरल कीजिए: 5^4 × 5^3

  1. 25^7
  2. 5^7
  3. 5^12
  4. 5^8
Answer: 5^7. aᵐ × aⁿ = aᵐ⁺ⁿ, so the power is 4 + 3 = 7. Answer: 5^7.
aᵐ × aⁿ = aᵐ⁺ⁿ, अतः घात 4 + 3 = 7। उत्तर: 5^7।
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