Q&A for How to Calculate a Square Root by Hand

Yes. A "perfect" number is a positive integer which is the sum of all of its positive divisors (except itself). Thus, 28 = 1 + 2 + 4 + 7 + 14.

.011. If you are calculating it by hand, here's what to do: 121's sqrt is 11. To get .000121, you simply find an amount of 0's after the decimal point and the number 11 afterwards. Then multiply by itself. .011*.011= .000121.

No, it's (x)^1/3.

It is the "imaginary" number 2i√2.

BODMAS is an acronym to help you remember the proper order of operations in evaluating an algebraic expression. B means "brackets": do everything inside brackets, braces or parentheses first; O means "orders" (powers and roots); DM means "divide and multiply" (left to right); and finally, AS means "add and subtract" (also left to right).

√169 = 13.

First cube 3.5, then find the square root of that number.

Take a quiz on the internet regarding about that topic. Try to solve examples given by your instructor.

14.

Use a calculator. Otherwise, you're stuck with the method shown above.

At the end of the eight you must place a zero next to it. No matter what, your number must be separated in pairs starting from the decimal place, evaluate it as 354.80, and break up the pairs as follows: 3,54,80 etc and keep adding pairs of zeroes after 80. Don't forget to place the decimal place properly in your solution, and be sure to not include the decimal when you are doubling the solution to find the next digit.

Without a calculator, you would go through the process of estimation: we know that 100² = 10,000, so the answer is well above 100. 150² = 22,500, so that's too high. 140² = 19,600, so we're getting closer. 135² = 18,225, so we're really close. 134² = 17,956, so that's a little low. 134.5² =18,090.25, still just a little low. 134.6² = 18,117.16, so the answer is slightly less than halfway between the last two guesses. 134.54² = 18,101, so with a bit more estimating, we can say that √18,100 is approximately 134.537. This process can involve a great deal of multiplication. That's why it's nice to have a calculator.

Let's assume you want to do this by hand. We know that the square root of 10,000 is 100. Therefore, the number we're looking for is slightly above 100. By trial and error we discover that 100.01 is too low and that 100.02 is just slightly low. If we square 100.025, we find that that's just perfect.

The square root of 441 is 21 because 21 x 21 is equal to 441. 21 x 20 is 420, and 21 x 1 = 21. 420 + 21 = 441.

The square root of 25 is 5. The square root of 16 is 4. The square root of 9 is there. 5 + 4 + 9 = 18.

1.612.

It's doubtful that anyone has ever been able to calculate the tenth root of 5 manually. It would take a computer to do that.

Consult a logarithm table or simply ask a search engine.

√(x / 1200) = √x / √1200 = √x / 34.64.

Most calculators come with a square root key. √16 = 4.

Yes, in most cases.

Yes. Because zero is considered an integer (a whole number), its square (which is also zero) is called a "perfect square."

There is no easier method that is as accurate as the above method. "Newton's method" is superficially easier, but it is generally slower and usually less accurate.

No. "Perfect square" means the square of a whole number. 980 is the square of 31.304951.

The answer is approximately 80.007. For square roots of decimals, you can always use a calculator.

The square root of 5/3 is equivalent to the square root of 5 divided by the square root of 3. If you calculate these square roots you will find that the square root of 5/3 is 2.24/1.73 or about 1.291.

No, you cannot use this method for solving cube roots. If you are solving cube roots, it is better to use a different method or to use you calculator.

Draw a tree diagram first and you find out all of the factors of 10. 10- 2,5. If there are doubles of factors, you but one of the number on the outside. Is there are no repeats of a number, it is the simplest it can be. In the case √10 is the simplest that it can be.

Yes, approximately.

√81 + √25 = 9 + 5 = 14.