how do you take the square root of a round number?
372510
this is actually very complicated and I had never thought about it before. everyone always just uses their calculator. see this website for several methods of doing it manually.
78107
what is the square root of orange?
98145
the square root of 2 is 1.4142
256504
because 56 is not an even root the best answer is=\n(n-squareroot of 56)(n+squareroot of 56). \nThe square root of 56 is 7.48331477355 if you need the exact number, but that's messy.
408683
When we square a number we multiply it by itself\n\nThe square root of a number is the number that when multiplied by itself makes that number.\n\nFor example:\n\nThe square root of 9 is 3 (3 * 3 = 9)\n\nThere are different ways of finding the square rot of a number (by hand - using a calculator is just too easy lol) and the source below shows you some of them.
706596
You'd have to use the chain rule for the square root, then the quotient rule for what's inside.\n\nf ' (x) = (1/2) [(2x³ - 7) / (4x + 1)]^(-1/2) times the derivative of the radicand.\nFor that, the quotient rule gives:\n[6x²(4x + 1) - 4(2x³ - 7)] / (4x + 1)²\n\nThere's most likely some simplifying to be done, but that should get you on the right path.\n\nGood luck!
771462
The answer is +/- the square root of 119, over 8.  Divide both sides of the equation by 8, and you get X squared = 119/64.  Take the square root of this and you have the answer.  64 is a perfect square, but 119 isn't.  If it had been 121 on top, your answer would be +/- 11/8.
1002104
there is no direct way.  A way of doing it though, would be for exampe, if you have 45.385, take the 45 as the whole number, and what u are left with .385, do 1 devided by 0.385, which gives you 2.59, so 2.6 rounded, now just multiply both by 10, and VOILA! 45 10/26\n\nSo basicaly devide "1" by the decimal, and multiply by 10, and put 10 over that answer!\n\nhope that helped
852187
Saw your edit, see below...\n\nSo if I understand correctly, you start with a decimal number that has a finite number of decimals, like 0.41 or 0.87293, and you want to know if you can build an irrational number that begins with those same decimals, expressing it as a function of integers only.\n\nIn your example, this can be done with 0.41, because sqrt(2) = 1.41421... (the left side of the decimal doesn't matter to you).\n\nSure then.  There are infinitely many ways to do this, but here's just one:\n\nGiven the number "0,a" having n decimals.  So for 0.41, a=41 and n=2.  Then the given number can be expressed as a/10^n.\n\nIf you take sqrt(2)=1.41421... and divide it by 10 often enough, you'll get the number 0.000...0141421... which is irrational.  All you need to do then is add this to the original number.  Just make sure the first 1 appears on the (n+1)th decimal so as not to perturb the first n decimals.  This means dividing by 10^(n+1).\n\nSo the number a/10^n + sqrt(2)/10^(n+1) satisfies the conditions.  Everything is there is integers.\n\nIn the 0.41 case, this would yield the solution 41/100 + sqrt(2)/1000 = 0.41141421356...\n\nEdit: So you don't like it because it uses a.  OK, how about this:\n\nDefine "0,x" as the square of "0,a".  By adding an extra decimal to "0,x" and taking its square root, you will get "0,a" plus an irrational component.  This can be expressed as \n\nsqrt(x/10^n+1/10^(n+1))\n\nwhere n is the number of decimals for "0,x".  In the 0.41 example, this yields the number sqrt(1681/10000 + 1/100000) = sqrt(0.16811) = 0.410012194...
54004
11\n\n\n11 multiplied by 11 equals 121. So, the square root of 121 is 11.
960702
To take the square root of 625, the calculator would multiply by 5 to yield:\n\n3125\n\nThen it would start subtracting 100s+5 100s+15... from the leftmost digits: (s started at 0)\n\n3125\n 500-\n1500-   : 2 subtractions so first digit is 2 (so s is now 2)\nleaving 1125\n\nThen it subtracted 100s+5, 100s+15... (s = 2)\n\n1125\n 205-\n 215-\n 225-\n 235-\n 245- : 5 subtractions (so d is 5 which is appended to s yielding 25)\n        leaving 0\n\nSo the root of 625 is 25.
1031543
There is no exact square root but it is\n\n7414.85009963114
218797
sqrt(157452304)= +/-12548\n\ndon't forget that 2 negatives cancel out so every number has 2 square roots (either rational or irrational) , one positive and one negative.
154621
If you mean 100 inside a square root symbol, the answer is 10.  However, if you mean the true square roots (as opposed the result of the square root function) the answer is 10 or -10.
1187142
maybe something like 7^(1/3) over 7^(1/2)\n\nthat's the same as the cube root of 7 over the square root of 7.\nTo solve it, you would just subtract the exponents and you'd get 1 over 7^(1/6)\n\nI hope that is what you are looking for.
241586
Hello !\n\nA good question.\nSomething like:\n( round((sqrt(9!)) / 9 )  ) x (9/9)\n\n\n© ßogdan @ CyE CORP.
708801
The answer is 10\n\nMultiply 5 times 20 and take the square root of that.\n\nMultiplication and Square Roots can be done in either order.