Evaluate square root of 28+ square root of 63

Problem

√(,28)+√(,63)

Solution

1. Identify the radicands and look for perfect square factors for each term.

2. Factor the first term by expressing 28 as the product of its largest perfect square factor and another integer.

√(,28)=√(,4⋅7)

3. Factor the second term by expressing 63 as the product of its largest perfect square factor and another integer.

√(,63)=√(,9⋅7)

4. Simplify the radicals by taking the square root of the perfect square factors.

√(,4⋅7)=2√(,7)

√(,9⋅7)=3√(,7)

5. Combine the like terms by adding the coefficients of the common radical √(,7)

2√(,7)+3√(,7)=5√(,7)

Final Answer

√(,28)+√(,63)=5√(,7)

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