Maharashtra Board Class 7 Chapter 6 Set 30 Indices Solutions

Question 1. Find the square root:
(i) 625
(ii) 1225
(iii) 289
(iv) 4096
(v) 1089
Answer:
(i) 625

\( \therefore \) 625 = \( 5 \times 5 \times 5 \times 5 \)
\( \therefore \sqrt{625} = 5 \times 5 = 25 \)
(ii) 1225

\( \therefore \) 1225 = \( 5 \times 5 \times 7 \times 7 \)
\( \therefore \sqrt{1225} = 5 \times 7 = 35 \)
(iii) 289

\( \therefore \) 289 = \( 17 \times 17 \)
\( \therefore \sqrt{289} = 17 \)
(iv) 4096

\( \therefore \) 4096 = \( 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \)
\( \therefore \sqrt{4096} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \)
= 64
(v) 1089

\( \therefore \) 1089 = \( 3 \times 3 \times 11 \times 11 \)
\( \therefore \sqrt{1089} = 3 \times 11 \)
= 33 In simple words: To find the square root, we perform prime factorization of the given number. Then, we group identical prime factors into pairs and take one factor from each pair to multiply them together, which gives us the square root.

🎯 Exam Tip: Showing the prime factorization table step-by-step is crucial for full marks. Ensure all prime factors are correctly identified and grouped.

Maharashtra Board Class 7 Maths Chapter 6 Indices Practice Set 30 Intext Questions and Activities

Question 1. Try to write the following numbers in the standard form. (Textbook pg. no. 48)
(i) The diameter of Sun is 1400000000 m.
(ii) The velocity of light is 300000000 m/sec.
Answer:
(i) \( 1400000000 \, m = 1.4 \times 10^9 \, m \)
(ii) \( 300000000 \, m/s = 3.0 \times 10^8 \, m/sec \)
In simple words: Standard form (scientific notation) expresses large numbers as a product of a number between 1 and 10 and a power of 10, making them easier to read and understand.

🎯 Exam Tip: Count the number of places the decimal point is moved to the left to determine the positive power of 10. Always ensure the first part of the number is between 1 and 10 (inclusive of 1, exclusive of 10).

Question 2. The box alongside shows the number called Googol. Try to write it as a power of 10. (Textbook pg. no. 48)
ℹ️ चित्र व्याख्या (Diagram Explanation): एक बॉक्स में 'Googol' शब्द लिखा है, जिसके नीचे 1 के बाद 100 शून्य (\(10^{100}\)) की एक बहुत लंबी संख्या दर्शाई गई है। यह संख्या 'Googol' का संख्यात्मक प्रतिनिधित्व करती है, जिसे 10 की घात 100 के रूप में लिखा जाता है।
Answer:
\( 1 \times 10^{100} \) In simple words: A Googol is a very large number defined as 1 followed by 100 zeros, which can be compactly written as 10 raised to the power of 100.

🎯 Exam Tip: Understanding the concept of powers of 10 is essential for representing extremely large or small numbers in a concise manner. The power indicates how many zeros follow the 1 for whole number powers.