Finding the square root

How do I find the square root of 1345?

1345 can be simplified to sqrt(25)*sqrt(269) and as sqrt(25)= 5 This can be simplified to 5*sqrt(269) as 269 has no factors
Joe W.
30 April 2018
We cannot convert 1345 into a simplest radical form, since 1345=5x269 hence sqrt1345= (sqrt5)x(sqrt269) and both these square roots are irrational numbers.  Therefore 1345 cannot be reduced.
01 May 2018
02 May 2018
03 May 2018
1345 is not a perfect square. It’s factors are 1, 5, 269 and 1345. 5 and 269 are prime numbers, hence not perfect square either.To find the square root of 1345, you will get decimals present. Hence, square root of 1345 to 3 decimal places is 36.674.
Joy O.
21 May 2018
25 May 2018
Interpreting the question as 'approximate sqrt(1345) with pen and paper'... To get the result to the same accuracy as below using a method that is (a) a bit faster and more compact, and (b) on the A-level syllabus, use the generalised binomial expansion [proof not included - pursue if interested!]. The first order expansion of sqrt(1-x) is 1-x/2, so find: sqrt(1345)=sqrt(1369-24)=37*sqrt(1-24/2369) =37(1-12/1369)=36.67...The penultimate stage of the working above gives you a rational approximation for free, i.e. 1357/37.Hope that's of use even if a bit late to the party.
Peter T.
31 May 2018
*typo, should have 24/1369 not 24/2369
Peter T.
31 May 2018
In mathematics, a square root of a number a is a number y such that y² = a, in other words, a number y whose square (the result of multiplying the number by itself, or y * y) is square root of 1345 = 36.67
15 June 2018
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