Calculate the square root of 5625

Problem

√(,5625)

Solution

1. Identify the number as a perfect square ending in 25 which suggests its square root will end in 5

2. Determine the tens digit by looking at the first two digits, 56

3. Find the largest integer n such that n*(n+1)≤56 Since 7×8=56 the tens digit is 7

4. Combine the digits to find the candidate root, 75

5. Verify the result by squaring 75

75=(70+5)2

75=4900+2*(70)*(5)+25

75=4900+700+25

75=5625

Final Answer

√(,5625)=75

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