Calculate the square root of 150

Problem

√(,150)

Solution

1. Identify the number inside the radical and look for its prime factors.

150=2⋅3⋅5⋅5

2. Group the prime factors into pairs of perfect squares.

150=25⋅6

3. Apply the product property of radicals, which states √(,a⋅b)=√(,a)⋅√(,b)

√(,150)=√(,25⋅6)

4. Simplify the square root of the perfect square.

√(,25)⋅√(,6)=5√(,6)

Final Answer

√(,150)=5√(,6)

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