The square root of a number is really easy to find. Let's remember first that finding the square root of a number is the opposite of finding the exponent of a number. Moreover, we are only going to deal with positive square roots, a negative square root will result on imaginary numbers. In this article we are going to learn the steps to find the square root of any number without a calculator.

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Practice with other numbers

Square roots should always be positive when dealing with real numbers, that means you should not have a negative inside the square root. For example: if you have a negative outside the square root then you have -√16= -4 but if you have a negative inside the square root, you will get an imaginary number , √-16 =4i (an imaginary number) WATCH THIS ARTICLE AS A VIDEO AT WWW.I-HATE-MATH.COM

How do I find the square root of a number? Let's say we need to find the square root of 320. Well, your main goal is to find the factors of 320, that means the numbers that composed 320, then organize them by perfect squares (ie 16,25,36,81,100, etc) For example: 320= 2_2_2_2_2_2_5, now organize them by perfect squares (the ones you can not make a perfect square just leave it alone) 320= 4_4_4_5 or 320=16_4*5

Once you have the factors, get the square root of each number separately . In this case you can get the square root of 16=4, the square root 4=2, and the square root of 5, since square root of 5 does not have a perfect square is left the same way . Now, just multiply your answers 4_2_√5=8√5.

As you can see √320=8√5

If you want to find the approximate value of 8√5, you need to find the value of √5, well think of an easy square root you know, for example √4=2, therefore, √5≅2.2. Now going back to your problem: 8√5≅8*(2.2)≅ 17.6

You can do this with any number: For example: √90 then find a square root close to √90, like √81= 9, so √90 ≅9.4 √27≅5.1 (from √25=5) √43≅ 6.5 (from √49=7)

Another example, How to find the square root of 4000? You follow the same steps as before, enlarge the picture and you will see step by step. Now you can find the square root of any number.

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- Vanessa Graulich, www.I-hate-math.com