If I ask you how to calculate a square root , your answer will surely be “that’s why the calculator exists”, however, this is knowledge that we all must have, regardless of the technological era we live in. That is why this time we will tell you how to calculate the square root of 3.
About the square root of 3
The square root of 3 yields a positive, real number, which when multiplied by itself yields the number.
In detail, the number resulting from calculating the root of three is 1.7320508075, considering ten decimal places. This number is an irrational number, so it is a number that cannot be expressed as a fraction, because the decimal numbers continue infinitely.
At the same time, the square root of three is equal to the length of the sides of a hexagon whose flat sides measure one.
In turn, the square root of three is equal to the value of the diagonal of a cube whose sides measure one, this can be demonstrated using the Pythagorean theorem.
Instructions to do the square root of 3
Calculating the square root of a number without using a calculator is not impossible, although the opposite may have crossed your mind. We explain below how to achieve it:
- The first thing is to look for a number that, when multiplied by itself, results in a number close to three, below. For example, one multiplied by itself is one.
- Now we will look for a number that, when multiplied by itself, results in a number close to three, above. For example, two multiplied by itself is four.
- So, we know that the root of three is a number between one and two.
- The next thing will be to look for a number between one and two that, when multiplied by itself, results in a number close to three, below. For example, 1.7, multiplied by itself is 2.89.
- Now we will look for a number between one and two that, when multiplied by itself, results in a number close to three, above. For example, 1.8, multiplied by itself is 3.24.
- So, we know that the root of three is a number between 1.7 and 1.8.
- We must look for a number between 1.7 and 1.8 that, when multiplied by itself, results in a number close to three, below. For example, 1.73, multiplied by itself is 2.9929.
- The next thing will be to look for a number between 1.7 and 1.8 that, when multiplied by itself, results in a number close to three, below. For example, 1.74, multiplied by itself is 3.0276.
- So, we know that the root of three is a number between 1.73 and 1.74.
So we could continue adding decimals to find a value that is fairly close to three.
Tips for Doing the Square Root of 3
Some recommendations to take into account when calculating the value of the square root of 3 are:
- Remember that the square root of 3 is an irrational number, so even if you apply the instructions that we have given you before, you will never be able to obtain an exact result, only a result with the number of decimal places decided by you.
- Due to the previous recommendation, we advise you to place a limit number of decimals, in this way you will not have to apply the method that we have taught you infinitely.
- By having a limit of decimals established, you can make an approximation of the result. For example, if we say we want a single decimal and we know from the method taught that the root of three is a number between 1.73 and 1.74, we could round and say that the root of three equals 1.7.