Class 9 Exam > Class 9 Questions > If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷...
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If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating?
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If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, t...
To simplify the expression A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶, we can use the rule of exponents which states that when multiplying powers with the same base, we add their exponents. Additionally, we can simplify the square roots using the rule that the square root of a product is equal to the product of the square roots.
1. Simplify the powers of √8:
(√8)⁴ x (√8)⁶ x (√8)¹⁰
= (√8)⁴+⁶+¹⁰
= (√8)²⁰
= 8¹⁰
2. Simplify the powers of √2:
(√2)⁸ x (√2)⁷ x (√2)⁶
= (√2)⁸+⁷+⁶
= (√2)²¹
= 2¹⁰.5
3. Simplify the expression A:
A = 8¹⁰ x 2¹⁰.5
= (2³)¹⁰ x 2¹⁰.5
= 2³⁰ x 2¹⁰.5
= 2³⁰+¹⁰.⁵
= 2⁴⁰.⁵
Now, let's simplify √2 x A:
√2 x A = √2 x 2⁴⁰.⁵
Since the square root of 2 is irrational, multiplying it by any rational number will result in an irrational number. Therefore, the product √2 x A is irrational.
Hence, the answer is B. Irrational.
1. Simplify the powers of √8:
(√8)⁴ x (√8)⁶ x (√8)¹⁰
= (√8)⁴+⁶+¹⁰
= (√8)²⁰
= 8¹⁰
2. Simplify the powers of √2:
(√2)⁸ x (√2)⁷ x (√2)⁶
= (√2)⁸+⁷+⁶
= (√2)²¹
= 2¹⁰.5
3. Simplify the expression A:
A = 8¹⁰ x 2¹⁰.5
= (2³)¹⁰ x 2¹⁰.5
= 2³⁰ x 2¹⁰.5
= 2³⁰+¹⁰.⁵
= 2⁴⁰.⁵
Now, let's simplify √2 x A:
√2 x A = √2 x 2⁴⁰.⁵
Since the square root of 2 is irrational, multiplying it by any rational number will result in an irrational number. Therefore, the product √2 x A is irrational.
Hence, the answer is B. Irrational.
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If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating?
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If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating?.
If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = (√8)⁴ x (√8)⁶ x (√8)¹⁰ x (√2)⁸ x (√2)⁷ x (√2)⁶ is simplified, then √2 x A =? A. rational B. Irrational C. Non terminating non repeating D. Terminating repeating?.
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