Evaluate - square root of 68 square root of 407

Problem

√(,68)√(,407)

Solution

1. Combine the square roots using the product property of radicals, √(,a)√(,b)=√(,a*b)

√(,68⋅407)

2. Multiply the numbers inside the radical.

68⋅407=27676

√(,27676)

3. Factor the radicand to identify perfect square factors.

68=4⋅17

407=11⋅37

√(,4⋅17⋅11⋅37)

4. Simplify the radical by taking the square root of the perfect square factor 4

2√(,17⋅11⋅37)

5. Multiply the remaining prime factors inside the radical.

17⋅11⋅37=6919

2√(,6919)

Final Answer

√(,68)√(,407)=2√(,6919)

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