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
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.
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.
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.
*typo, should have 24/1369 not 24/2369
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 a.so square root of 1345 = 36.67