if 7 is a prime number than prove √7 is a irrational number
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If further implies that b2 is also divisible by 7. And Hence, we can say that b is also divisible by 7. Therefore, it implies that aand b have at least one common factor that is 7. Which implies that, √7 is an irrational number
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In this question we have given 7is a prime number and let us assume that √7 is a rational number. As we know that any rational number can be represented in pqform ; q≠0. Now multiply by b on both sides we get, √7b=a. ... Which implies that, √7 is an irrational number.
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