Real Numbers | Complete NCERT BACK EXERCISE in 1 Video | Class 10th Board
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- เผยแพร่เมื่อ 3 ก.ค. 2024
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✨ Topics covered ✨
00:00 - Introduction
01:48 - Exercise - 1
01:06:00 - Exercise - 2
01:27:47 - Thank You !
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1:27:29 -
(ii) 7√5
Let us assume that 7√5 is a rational number.
Then, 7√5 = a/b, where a and b have no common factors other than 1.
(7√5) b = a
√5 = a/7b
Since, a, 7, and b are integers, so, a/7b is a rational number. This means √5 is rational. But this contradicts the fact that √5 is irrational.
So, our assumption was wrong. Therefore, 7√5 is an irrational number.
(iii) 6 + √2
Let us assume that 6 + √2 is rational.
Then, 6 + √2 = a/b, where a and b have no common factors other than 1.
√2 = (a/b) - 6
Since, a, b, and 6 are integers, so, a/b - 6 is a rational number. This means √2 is also a rational number.
But this contradicts the fact that √2 is irrational. So, our assumption was wrong.
Therefore, 6 + √2 is an irrational number.
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