Evaluate ( square root of 10)/( square root of 3)

Problem

√(,10)/√(,3)

Solution

1. Apply the quotient property of radicals to write the expression as a single square root.

√(,10)/√(,3)=√(,10/3)

2. Rationalize the denominator by multiplying both the numerator and the denominator by √(,3) to remove the radical from the bottom.

√(,10)/√(,3)⋅√(,3)/√(,3)

3. Multiply the numerators using the product property of radicals, √(,a)⋅√(,b)=√(,a*b)

√(,10)⋅√(,3)=√(,30)

4. Multiply the denominators to simplify the expression.

√(,3)⋅√(,3)=3

Final Answer

√(,10)/√(,3)=√(,30)/3

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