![]() We already know if 138 is a perfect square so we also can see that √138 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 138 is a perfect square. Is The Square Root of 138 Rational or Irrational?Ī common question is to ask whether the square root of 138 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 138 is not a perfect square. In math, we refer to 138 being a perfect square if the square root of 138 is a whole number. √138 = q × q = q 2 Is 138 a Perfect Square? This is very useful for long division test problems and was how mathematicians would calculate the square root of a number before calculators and computers were invented.So what is the square root? In this case, the square root of 138 is the quantity (which we will call q) that when multiplied by itself, will equal 138. √360 = 360 ½ How to Find the Square Root of 360 Using Long Divisionįinally, we can use the long division method to calculate the square root of 360. ![]() Let's see how to do that with the square root of 360: ≈ 18 97/100 What is the Square Root of 360 Written with an Exponent?Īll square root calculations can be converted to a number (called the base) with a fractional exponent. However, we can make it into an approximate fraction using the square root of 360 rounded to the nearest hundredth. Like we said above, since the square root of 360 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: √360 ≈ 18.974 What is the Square Root of 360 as a Fraction? Sometimes you might need to round the square root of 360 down to a certain number of decimal places. On a computer you can also calculate the square root of 360 using Excel, Numbers, or Google Sheets and the SQRT function, like so: √360 ≈ 18.9737 How to Calculate the Square Root of 360 with a Computer On most calculators you can do this by typing in 360 and then pressing the √x key. If you have a calculator then the simplest way to calculate the square root of 360 is to use that calculator. How to Calculate The Square Root of 360 with a Calculator In this example, the square root of 360 can be simplified. This is a process that is called simplifying the surd. Can the Square Root of 360 Be Simplified?ģ60 can be simplified only if you can make 360 inside the radical symbol smaller. We already know if 360 is a perfect square so we also can see that √360 is 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 360 is a perfect square. Is The Square Root of 360 Rational or Irrational?Ī common question is to ask whether the square root of 360 is rational or irrational. In this case, as we will see in the calculations below, we can see that 360 is not a perfect square. In math, we refer to 360 being a perfect square if the square root of 360 is a whole number. √360 = q × q = q 2 Is 360 a Perfect Square? ![]() ![]() So what is the square root? In this case, the square root of 360 is the quantity (which we will call q) that when multiplied by itself, will equal 360.
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