Solutions to the Above Questions

Write 25 and 125 as the product of prime factors: 25 = 5^{2} and 125 = 5^{3}, hence

Write 64 and 16 as the product of prime factors: 64 = 2^{6} and 16 = 2^{4}, hence

Use product rule

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

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

Write the radicand as a square and simplify

Write the radicand as the product of $2$ and a square and simplify

Simplify the radicand
Write as the product of prime factors and simplify

Since n is a positive integer, then N = 2 n + 1 is an odd integer. Hence

Since n is a positive integer, then N = 2 n is an even integer. Hence


Use division rule and simplify the radicand

Multiply numerator and denominator by the conjugate of the denominator
Expand and simplify
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