Evaluate ( square root of 5)/( square root of 2)

Problem

√(,5)/√(,2)

Solution

1. Identify the expression as a fraction with a radical in the denominator that needs to be rationalized.

2. Apply the property of radicals to combine the numerator and denominator under a single square root or prepare for multiplication.

√(,5)/√(,2)

3. Multiply both the numerator and the denominator by √(,2) to eliminate the radical from the denominator.

(√(,5)⋅√(,2))/(√(,2)⋅√(,2))

4. Simplify the numerator using the product rule for radicals, √(,a)⋅√(,b)=√(,a*b) and simplify the denominator.

√(,10)/2

Final Answer

√(,5)/√(,2)=√(,10)/2

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