Calculate the 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)=√(,(2)2⋅15)

4. Extract the square root of the perfect square from under the radical.

√(,240)=2√(,15)

5. Simplify the coefficient outside the radical.

√(,240)=4√(,15)

Final Answer

√(,240)=4√(,15)

Want more problems? Check here!