Simplify square root of (21-(-4))^2+(25-5)^2

Problem

√(,(21−(−4))2+(25−5)2)

Solution

1. Simplify the terms inside the first set of parentheses by handling the double negative.

√(,(21+4)2+(25−5)2)

2. Evaluate the subtractions and additions inside both sets of parentheses.

√(,(25)2+(20)2)

3. Square the resulting numbers.

√(,625+400)

4. Add the values inside the square root.

√(,1025)

5. Factor the number under the radical to simplify the square root, noting that 1025=25×41

√(,25×41)

6. Extract the square root of the perfect square factor.

5√(,41)

Final Answer

√(,(21−(−4))2+(25−5)2)=5√(,41)

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