Solutions to the Above Questions
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Write 25 and 125 as the product of prime factors: 25 = 52 and 125 = 53, hence
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Write 64 and 16 as the product of prime factors: 64 = 26 and 16 = 24, hence
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Use product rule
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Convert the mixed number under the radical into a fraction and substitute
Use the division formula for radicals
Write 64 and 27 as product of prime factors, substitute and simplify
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Use the product formula and write 34 as the product of prime factors
Simplify
For √(17 x) and √(34 x) to be real numbers, x must be positive hence |x| = x
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Write the radicand as a square and simplify
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Write the radicand as the product of $2$ and a square and simplify
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Simplify the radicand
Write as the product of prime factors and simplify
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Since n is a positive integer, then N = 2 n + 1 is an odd integer. Hence
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Since n is a positive integer, then N = 2 n is an even integer. Hence
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Use division rule and simplify the radicand
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Multiply numerator and denominator by the conjugate of the denominator
Expand and simplify
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