What is 72 times its square root?

A perfect square is a number whose square root is an integer. This means it’s the result of multiplying an integer by itself. When adjusted to four significant numbers, the square root of 72 is 8.485 in decimal form. Because it isn’t a square or perfect square, you can use a scientific calculator to solve it rapidly. If this option is not available, there are a few other options you can consider. If this option is unavailable, there are a few strategies you might employ to arrive at a solution.

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Using Two Reference Numbers to Multiply

You’ll need to know the two closest perfect squares surrounding the number 72 to find the square root of 72. Our numbers are 8 and 9 in this example. The number 72 lies between the squares of 8 and 9, which are 64 and 81.

Divide 72 by 8 or 9 after that. Depending on the number used to split it, the result will be 9 or 8. Then calculate the mean of the result and the original square, which is (9+8)/2=8.5. Finally, repeat the first two stages until you achieve the appropriate level of precision.

Radical Form Simplified

Simplifying a radical until no further square roots, cube roots, fourth roots, and so on can be found is known as simplified radical form. It also entails the elimination of radicals from a fraction’s denominator. By dividing the radicand into a product of known factors, the square root of 72 can be simplified. To begin, locate the highest square that divides evenly into 72. The number in this example is 36. As a result, 72 can be stated as 36 x 2, and the steps are as follows:

√ 72 = √2x√36 = √2x√62 = 6√ 2

Multiplication by Cross

The approach is used to calculate a square root’s exact answer. When there are even numbers of digits, multiply the first by the last, the second by the second last, and so on until all of the digits have been multiplied. Find the total and multiply it by two. Repeat the process until you reach the middle digit with an odd number of digits. Find the total of the answers and multiply it by two. The middle digit is then squared and added to the total.

Method of Long Division

Begin by pairing up the digits, starting with the units digit. A period is the created pair and any remaining digit (if any). Use the largest square number equal to or slightly less than the first period as both the divisor and the quotient after determining the largest square number. Multiply the divisor and quotient together, then subtract the result from the first period. Then, to the right of the remainder, write the following period. As a result, a new dividend has been established. The new dividend is established.

The new divisor is found by multiplying the quotient by two and adding an ideal digit that acts as the quotient’s next digit. The number, such as the digit’s product, is picked, with the new divisor’s value equal to or slightly less than the new dividend. Finally, repeat steps 2 through 4 until all of the periods have been included or taken up. The requisite square root of the supplied number is obtained as the quotient.

Misha Khatri
Misha Khatri is an emeritus professor in the University of Notre Dame's Department of Chemistry and Biochemistry. He graduated from Northern Illinois University with a BSc in Chemistry and Mathematics and a PhD in Physical Analytical Chemistry from the University of Utah.


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