Free Square Root of 90 Answer

Square root of 90

When looking for the Square root of 90, we have to note that it is not a perfect square. The good news is that it is a semi perfect number, meaning it is the sum of all, or most of it’s divisors. 


To work out the square root of 90 (which I will do for you below), you are raising 90 to the power of half. Below I will demonstrate with the long division method, and the approximation methods.


What is the Square Root of 90?


The value of the square root of 90 is 9.486832980505138.


Is the Square root of 90 Rational, or irrational?


When defining rational and irrational numbers, a rational number is a number that can be shown in the form of a quotient, or in other words a division of two integers. Based on this information, we know that 90 is irrational. 


The methods of finding the Square Root of 90




Approximation is approximating your sum, up to the nearest whole decimal. For example, 9.486832980505138 would be rounded up to 9.5.


  • Find your 2 perfect squares, that are closest to 90. These are 81 and 100. 81 < 90 < 100.
  • √81 < √90 < √100
  • 9 < √90 < 10
  • Divide your sum of 90 by 9 or 10, which equals 10.
  • Find the average of this and the 9, which would be 10 + 9 / 2
  • This equals 9.5. Thus the final answer is 9.5.


Long Division


  • Write your square root base numerically in pairs, 90. 00 00 00.
  • Find the number x that gives 90, or less. We can find that 9×9=81, so we can subtract 81 from 90 and 9 remains.
  • Bring the next pair of zero’s down, so we have 900.
  • Multiply the amount obtained in the previous step with 2 to create 18. Now 180 is set in the new divisor place. 
  • Find a number to be added in place with 180, such as that the sum when multiplied creates 900 or less. Using this methodology, we determine 180+4=184 and 184×4=736.
  • Subtract the number you have from 900, which creates 164 and add your next pair of zeros. 16400 is our new numbered dividend. 
  • Repeat this process until we have the value at 3 decimal places. 
  • To conclude this method, it ends with 9.486.




The biggest tip I can give is to know that 90 is between the squares of 81 and 100, so the square root must lie between 9 and 10. 


Thank you for reading, if you want to see other Math content, I will be adding them quick and fast!

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