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sqrt5885=?

5885=? \sqrt{5885}=?

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Q. 5885=? \sqrt{5885}=?
  1. Find Prime Factorization: Find the prime factorization of 58855885 to simplify the square root.\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 keep going.\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 to simplify the square root.\newline5885=5×13×7×13\sqrt{5885} = \sqrt{5 \times 13 \times 7 \times 13}\newlineWe have a pair of 1313s, so we can take one 1313 out of the square root.\newline5885=13×5×7\sqrt{5885} = 13 \times \sqrt{5 \times 7}
  3. Multiply Remaining Numbers: Multiply the remaining numbers under the square root. 5×7=35\sqrt{5 \times 7} = \sqrt{35} So now we have: 5885=13×35\sqrt{5885} = 13 \times \sqrt{35}
  4. Write Final Simplified Form: Write the final simplified form of the square root. 5885=13×35\sqrt{5885} = 13 \times \sqrt{35}

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