What Is the Square Root of 72?

A number with an integer as its square root is referred to as a perfect square. This implies that it is the result of multiplying an integer by itself. When adjusted to four significant numbers, the square root of 72 is 8.485, or in decimal form. You can rapidly solve it with a scientific calculator because it is not a square or perfect square. There are a few approaches you can take if this option is not available to find a solution. There are a few techniques you might employ to find a solution if this choice is not an option.

Using Two Reference Numbers to Multiply

You must be aware of the two perfect squares that are the closest to the number 72 in order to calculate its square root. In this instance, our numbers are 8 and 9. Between the squares of 8 and 9, which are 64 and 81, respectively, is the number 72.

Thereafter, divide 72 by 8 or 9. Depending on the number chosen to divide it by, the answer will either be 9 or 8. Next, calculate the square’s initial value (9+8)/2, which is 8.5, and the mean of that result. Finally, keep going back and forth between the first two until you achieve the needed precision.

Radical Form with Simplicity

Simplifying a radical until no more square roots, cube roots, fourth roots, and so on are found is required to express a radical in simplified radical form. Radicals in a fraction’s denominator must also be eliminated. By dividing the radicand into a combination of known factors, the square root of 72 can be made simpler. Find the highest square that divides into 72 equal parts to start. In this instance, the answer is 36. Therefore, 72 can be written as 36 x 2, so continue as follows:

√ 72 = √2x√36 = √2x√62 = 6√ 2

Multiplication by Cross

The technique is used to determine the precise solution of a square root. If there are even numbers of digits, you must multiply the first digit by the last digit, the second by the next-to-last digit, and so on, multiplying each digit until all of them have been multiplied. Double the total after finding the sum. Use the same procedure until you reach the middle digit for an odd number of digits. Add the answers together, then multiply the result by two. The middle digit should then be squared and added to the total.

Method of Long Division

Starting with the units digit, continue pairing up the digits. A period is defined as the newly formed pair and any additional digits. Use the greatest square integer, which is equal to or slightly less than the first period, as the quotient and the divisor. Divide the divisor by the quotient, then take the result away from the first period. Next, add the subsequent period to the right of the remaining space. A fresh dividend is created as a result. The new dividend is then created.

The new divisor is now discovered by multiplying the quotient by two and then adding an ideal digit that serves as the quotient’s next digit. The chosen number is equal to or slightly less than the new dividend, such as the product of the digit and the new divisor. Finally, keep repeating steps 2, 3, and 4 until all periods have been included or taken up. The obtained quotient is the necessary square root of the supplied number.


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