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2sqrt5885

25885 2 \sqrt{5885}

Full solution

Q. 25885 2 \sqrt{5885}
  1. Identify Prime Factors: Identify the prime factors of 58855885. \newline5885=5×11775885 = 5 \times 1177\newlineBut 11771177 isn't a prime number, so we need to factor it further.\newline1177=13×911177 = 13 \times 91\newlineAnd 9191 is also not prime, so we keep factoring.\newline91=7×1391 = 7 \times 13\newlineNow we have all prime factors.\newline5885=5×13×7×135885 = 5 \times 13 \times 7 \times 13
  2. Group Prime Factors: Group the prime factors into pairs for square roots.\newlineWe have a pair of 1313s.\newlineSo, we can take 1313 outside the square root.\newline25885=2×13×5×72\sqrt{5885} = 2 \times 13 \times \sqrt{5 \times 7}
  3. Simplify Expression: Simplify the expression by multiplying the numbers outside the square root. \newline2×13=262 \times 13 = 26\newlineSo, 25885=26×352\sqrt{5885} = 26 \times \sqrt{35}
  4. Final Simplified Form: There are no more pairs of prime factors to simplify the square root. So, the final simplified form is: 26×3526 \times \sqrt{35}

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