You cannot.
There are some partial rules (eg a square cannot end in 3), but none exhaustive.
I'm assuming you're wondering if a number is a perfect square? Well, memorization will help as will guess and check. However, if you feel like doing it all by hand, simplifying the square will help you determine if it is a perfect square. Example: let's figure out if the number 225 is a perfect square. Let's take 225 and factor it. When you factor this number, you want to look at factoring numbers which are a perfect square in and of themselves. So 22 is 4, but that doesn't factor, how about 52 ? 25 will indeed factor, so we have 25*9 (look at that, 9 is also a factor). If we split it up like this, we have sqrt(25*9). We can take the square root of these individually and multiply them together. sqrt(25)*sqrt(9) = 5*3 = 15. Therefore 225 is a perfect square of 15.
Look at the two nearest perfect squares and determine which is closer7*7 = 498*8= 64It is closer to 8Roughly 7.6orYou can get a decent calculator that you can punch in and get the exact number
To square a number, you multiply it times itself, for example 3^2 = 3x3 = 9. To "undo" the squaring of a number, you determine its square root. In this case, the square root of 9, or √9. If the number is a perfect square, then the answer is the number that you have to square to get the number under the radical, √. For instance, √9 = 3 because 3^2 = 3x3 = 9. For numbers that are not perfect squares, or for any other number that you find difficult to work with, use your calculator. Different calculators have different keys and instructions, so you should read the instructions that came with your calculator, or look up the instructions online.
No. Look at the prime factors of 65: there are no repeated prime factors, therefore this number contains no perfect square.
perfect square of 16= 4 because 4 times 4 is 16.
The simplest way to do it is to use Logarithms, from a book of Logarithmic Tables and Anti-logarithms. You simply look up the Logarithm of your quantity, then divide that quantity by 2 , and then look up its Anti-logarithm. that will give you the answer.
As a general rule, you look to see if the number has any perfect squares as factors, but 274 doesn't have any of those. The square root of 274 is roughly 16.553.
I dont know too
I suggest you try to split the number up into prime factors. It should then be clear what the largest square factor is - simply look for repeated prime factors.
The word "difference" implies subtraction. The word "squares" implies a perfect square term or number. To recognize the "difference of squares" look for 2 perfect square terms, one being subtracted from the other. Ex. x2 - 16. "x" is being squared and 16 is a perfect square. They are being subtracted. Factors: (x+4)(x-4)
77 is not a perfect square. Another way to look at it is this (use a calculator) sqrt(77) ~= 8.774964387 Notice how there is no point where the numbers begin to repeat themselves (e.g., 1.222322232223) Both reasons tell us that sqrt(77) is an irrational number. ----------- Yes - the square roots of all non-perfect square integers (ie the numbers which are 1², 2², 3², ...) are irrational.
When you're asked to simplify the square root of something that isn't a perfect square like 25 or 16, look for perfect square factors within the number. For example, 75 can be written as 25x3. I'm sure you know 25 to be 5x5, the perfect square of 5. Now we can write 75 as 52x3. Since we're taking the square root, 52 gets moved out of the square root and you can write the final answer as 5 times the square root of 3, the factor that's left. Final answer: 5sqrrt3