In this short article we"re walking to calculation the square source of 72 and explore what the square source is and also answer some of the common questions friend might. We"ll also look at the different methods because that calculating the square source of 72 (both with and also without a computer/calculator).

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Square source of 72 Definition

In mathematical type we can display the square root of 72 utilizing the radical sign, like this: √72. This is usually described as the square root of 72 in radical form.

So what is the square root? In this case, the square root of 72 is the quantity (which we will contact q) that when multiplied by itself, will equal 72.

√72 = q × q = q2

Is 72 a Perfect Square?

In math, we describe 72 being a perfect square if the square root of 72 is a totality number.

In this case, as we will see in the calculations below, we deserve to see that 72 is no a perfect square.

Is The Square source of 72 reasonable or Irrational?

A usual question is come ask whether the square source of 72 is reasonable or irrational. Reasonable numbers have the right to be created as a portion and irrational number cannot.

A quick means to inspect this is to view if 72 is a perfect square. If the is, then it is a reasonable number. If it"s not a perfect square then it"s one irrational number.

We already know if 72 is a perfect square so we also can check out that √72 is an irrational number.

Can the Square source of 72 be Simplified?

72 can be simplified just if you can make 72 inside the radical price smaller. This is a process that is dubbed simplifying the surd. In this example, the square source of 72 have the right to be simplified.

√72 = 6√2.

How to calculate The Square root of 72 through a Calculator

If you have actually a calculator then the simplest method to calculate the square root of 72 is to use that calculator. On many calculators you can do this by inputting in 72 and also then pressing the √x key. Girlfriend should get the following result:

√72 ≈ 8.4853

How to calculate the Square root of 72 through a Computer

On a computer you can also calculate the square root of 72 using Excel, Numbers, or Google Sheets and also the SQRT function, like so:

SQRT(72) ≈ 8.485281374239

What is the Square source of 72 Rounded?

Sometimes you might need to ring the square source of 72 under to a certain number of decimal places. Here are the solutions to that, if needed.

10th: √72 ≈ 8.5

100th: √72 ≈ 8.49

1000th: √72 ≈ 8.485

What is the Square source of 72 as a Fraction?

We covered earlier in this short article that just a rational number can be written as a fraction, and also irrational numbers cannot.

Like we said above, because the square source of 72 is one irrational number, we cannot do it into precise fraction. However, we have the right to make it into an approximate portion using the square root of 72 rounded to the nearest hundredth.

See more: How Many Quarts Equal A Half Gallon ? How Many Quarts Of Oil Go In A Gallon

√72

≈ 8.5/1

≈ 849/100

≈ 8 49/100

What is the Square root of 72 Written with an Exponent?

All square root calculations can be convert to a number (called the base) with a fountain exponent. Let"s see just how to carry out that v the square source of 72:

√b = b½

√72 = 72½

How to uncover the Square root of 72 Using lengthy Division

Finally, we can use the long department method to calculation the square root of 72. This is an extremely useful because that long department test problems and was exactly how mathematicians would certainly calculate the square source of a number prior to calculators and computers were invented.

Step 1

Set up 72 in pairs of 2 digits from appropriate to left and also attach one collection of 00 due to the fact that we desire one decimal:


Step 2

Starting v the an initial set: the biggest perfect square less than or same to 72 is 64, and also the square source of 64 is 8 . Therefore, put 8 top top top and 64 at the bottom prefer this: