In this article we"re going to calculate the square root of 136 and explore what the square root is and answer some of the common questions you might. We"ll also look at the different methods for calculating the square root of 136 (both with and without a computer/calculator).
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Square Root of 136 Definition
In mathematical form we can show the square root of 136 using the radical sign, like this: √136. This is usually referred to as the square root of 136 in radical form.
So what is the square root? In this case, the square root of 136 is the quantity (which we will call q) that when multiplied by itself, will equal 136.
√136 = q × q = q2
Is 136 a Perfect Square?
In math, we refer to 136 being a perfect square if the square root of 136 is a whole number.
In this case, as we will see in the calculations below, we can see that 136 is not a perfect square.
Is The Square Root of 136 Rational or Irrational?
A common question is to ask whether the square root of 136 is rational or irrational. Rational numbers can be written as a fraction and irrational numbers cannot.
A quick way to check this is to see if 136 is a perfect square. If it is, then it is a rational number. If it"s not a perfect square then it"s an irrational number.
We already know if 136 is a perfect square so we also can see that √136 is an irrational number.
Can the Square Root of 136 Be Simplified?
136 can be simplified only if you can make 136 inside the radical symbol smaller. This is a process that is called simplifying the surd. In this example, the square root of 136 can be simplified.
√136 = 2√34.
How to Calculate The Square Root of 136 with a Calculator
If you have a calculator then the simplest way to calculate the square root of 136 is to use that calculator. On most calculators you can do this by typing in 136 and then pressing the √x key. You should get the following result:
√136 ≈ 11.6619
How to Calculate the Square Root of 136 with a Computer
On a computer you can also calculate the square root of 136 using Excel, Numbers, or Google Sheets and the SQRT function, like so:
SQRT(136) ≈ 11.661903789691
What is the Square Root of 136 Rounded?
Sometimes you might need to round the square root of 136 down to a certain number of decimal places. Here are the solutions to that, if needed.
10th: √136 ≈ 11.7
100th: √136 ≈ 11.66
1000th: √136 ≈ 11.662
What is the Square Root of 136 as a Fraction?
We covered earlier in this article that only a rational number can be written as a fraction, and irrational numbers cannot.
Like we said above, since the square root of 136 is an irrational number, we cannot make it into an exact fraction. However, we can make it into an approximate fraction using the square root of 136 rounded to the nearest hundredth.
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≈ 11 33/50
What is the Square Root of 136 Written with an Exponent?
All square root calculations can be converted to a number (called the base) with a fractional exponent. Let"s see how to do that with the square root of 136:
√b = b½
√136 = 136½
How to Find the Square Root of 136 Using Long Division
Finally, we can use the long division method to calculate the square root of 136. 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.
Set up 136 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
Starting with the first set: the largest perfect square less than or equal to 1 is 1, and the square root of 1 is 1 . Therefore, put 1 on top and 1 at the bottom like this: