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**

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.

**Tips**

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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