Square root of 3906·25 is

Concept: To find the square root of a decimal number, remove the decimal by multiplying it by a power of 100 to get a whole number, then check whether that whole number is a perfect square. If N 2 = M, then the square root of M is N. This works because multiplying by 100 = 102 scales both the number and its square root by a fixed factor of 10, which can be divided back out at the end.

1. Multiply 3906·25 by 100 to clear the decimal: 3906·25 × 100 = 390625.

2. Check whether 390625 is a perfect square. Since 625 × 625 = 390625, we have 390625 = 6252.

3. So 3906·25 × 100 = 6252, which means 3906·25 = (625/10)2 = 62·52.

4. Taking the square root of both sides: the square root of 3906·25 is 62·5.

Cross-check: expand (62 + 0·5)2 directly — 622 + 2 × 62 × 0·5 + 0·52 = 3844 + 62 + 0·25 = 3906·25, which matches the given number and confirms 62·5 is the required square root.