Like we said above, since the square root of 1345 is an irrational number, we cannot make it into an exact fraction. We covered earlier in this article that only a rational number can be written as a fraction, and irrational numbers cannot. Here are the solutions to that, if needed.ġ000th: √1345 ≈ 36.674 What is the Square Root of 1345 as a Fraction? Sometimes you might need to round the square root of 1345 down to a certain number of decimal places. On a computer you can also calculate the square root of 1345 using Excel, Numbers, or Google Sheets and the SQRT function, like so: √1345 ≈ 36.6742 How to Calculate the Square Root of 1345 with a Computer On most calculators you can do this by typing in 1345 and then pressing the √x key. If you have a calculator then the simplest way to calculate the square root of 1345 is to use that calculator. How to Calculate The Square Root of 1345 with a Calculator √1345 is already in its simplest radical form. In this example square root of 1345 cannot be simplified. This is a process that is called simplifying the surd. Can the Square Root of 1345 Be Simplified?ġ345 can be simplified only if you can make 1345 inside the radical symbol smaller. We already know if 1345 is a perfect square so we also can see that √1345 is an irrational number. If it's not a perfect square then it's an irrational number. Rational numbers can be written as a fraction and irrational numbers cannot.Ī quick way to check this is to see if 1345 is a perfect square. Is The Square Root of 1345 Rational or Irrational?Ī common question is to ask whether the square root of 1345 is rational or irrational. To find out more about perfect squares, you can read about them and look at a list of 1000 of them in our What is a Perfect Square? article. In this case, as we will see in the calculations below, we can see that 1345 is not a perfect square. In math, we refer to 1345 being a perfect square if the square root of 1345 is a whole number. √1345 = q × q = q 2 Is 1345 a Perfect Square? It should then be clear that computing any further will result in a number that would round to 1.403, making 1.403 the final estimate to 3 decimal places.So what is the square root? In this case, the square root of 1345 is the quantity (which we will call q) that when multiplied by itself, will equal 1345. If the number c returned is precise to the desired decimal place, stop. For a simpler, but less efficient method, continue to the following steps and example. For those with an understanding of series, refer here for a more mathematical algorithm for calculating n th roots. Estimating higher n th roots, even if using a calculator for intermediary steps, is significantly more tedious. While computing square roots entirely by hand is tedious.
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