Evaluate square root of 240

Problem

√(,240)

Solution

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

2. Factor the number 240 into its prime components.

240=2⋅120

240=2⋅2⋅60

240=2⋅2⋅2⋅30

240=2⋅2⋅2⋅2⋅15

240=2⋅3⋅5

3. Group the factors into perfect squares to simplify the radical.

√(,240)=√(,2⋅15)

√(,240)=√(,16⋅15)

4. Apply the product property of radicals √(,a⋅b)=√(,a)⋅√(,b)

√(,240)=√(,16)⋅√(,15)

5. Simplify the square root of the perfect square.

√(,16)=4

√(,240)=4√(,15)

Final Answer

√(,240)=4√(,15)

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