-2 and -3Check:(-2) + (-3) = -5(-2)(-3) = 6Thus -2 and -3 are not the required numbers. let's find them: x + y = -6xy = -5 y = -x -6x(-x - 6) = -5-x^2 - 6x = -5x^2 + 6x = 5x^2 + 6x + 9 = 5 + 9(x + 3)^2 = 14x + 3 = (+ & -)square root of 14x = -3 (+ & -)square root of 14x = -3 + square root of 14 or x = - 3 - square root of 14y = -x - 6y = 3 - square root of 14 - 6 or y = 3 + square root of 14 - 6y = -3 - square root of 14 or y = -3 + square root of 14Check:(-3 + square root of 14) + (-3 - square root of 14) = -6(-3 + square root of 14)(-3 - square root of 14) = -5 ?(-3)^2 - (square root of 14)^2 = -5 ?9 - 14 = -5Check also tow other numbers.
3 sqrt -5 = 3 x 5i = 15i; 3 sqrt 9 = 3 x 3 = 9 so full answer is 135i where i is the sqrt of -1
3*sqrt(5)*x
(x^2+x-1/2)= x(x+1)-1/2 [x + (1 - square root of 3)/2][x + (1 + square root of 3)/2] = 0 Check it: x^2 + x/2 + (square root of 3)x)/2 + x/2 + 1/4 + (square root of 3)/4 - (square root of 3)x/2 - (square root of 3)/4 - 3/4 = 0 x^2 + x/2 + x/2 + [(square root of 3)x]/2 - [(square root of 3)x]/2 + (square root of 3)/4 - (square root of 3)/4 + 1/4 - 3/4 = 0 x^2 + x - 2/4 = 0 x^2 + x - 1/2 = 0 How to find this roots: Using the completing the square method: x^2 + x - 1/2 = 0 x^2 + x = 1/2 x^2 + x + 1/4 = 1/2 + 1/4 (x + 1/2)^2 = 3/4 x + 1/2 = (plus & minus)(square root of 3/4) x = -1/2 + (square root of 3)/2 x = - 1/2 - (square root of 3)/2
root 27 = root 9 x root 3 = 3 root 3. Dividing this by root 3 gives 3!
5
-2 and -3Check:(-2) + (-3) = -5(-2)(-3) = 6Thus -2 and -3 are not the required numbers. let's find them: x + y = -6xy = -5 y = -x -6x(-x - 6) = -5-x^2 - 6x = -5x^2 + 6x = 5x^2 + 6x + 9 = 5 + 9(x + 3)^2 = 14x + 3 = (+ & -)square root of 14x = -3 (+ & -)square root of 14x = -3 + square root of 14 or x = - 3 - square root of 14y = -x - 6y = 3 - square root of 14 - 6 or y = 3 + square root of 14 - 6y = -3 - square root of 14 or y = -3 + square root of 14Check:(-3 + square root of 14) + (-3 - square root of 14) = -6(-3 + square root of 14)(-3 - square root of 14) = -5 ?(-3)^2 - (square root of 14)^2 = -5 ?9 - 14 = -5Check also tow other numbers.
It seems to be 25. Call your number "x". x = 5 square root of (5 square root of (5 ...) Square it; this will eliminate the outermost square root sign: x squared = 25 times 5 square root of (5 square root of (... Dividing the second equation by the first one, you get: x squared / x = 25 x / x x = 25
You can get a decimal approximation with a calculator, with Excel, etc. But if you want to keep it as a square root, the "standard form" is considered to be one that has no square roots in the denominator. In this case, to get rid of the square root in the denominator, you multiply both numerator and denominator by the square root of 5, with the following result: 3 / root(5) = 3 root(5) / root(5) x root(5) = 3 root(5) / 5 That is, three times the square root of 5, divided by 5.
A number that, when multiplied by itself, will result in a given number. The square root of four is two; the square root of one hundred is ten. 2 x 2= 4 ...........so 2 would be the square root of 4 3 x 3=9 ..........3 is square root 5 x 5=25 ...............5 get it?
root(x+5)-root(x-5)=2 root(x+5)=2-root(x-5) x+5=4-4root(x-5)+x-5 4root(x-5)+6=0 root(x-5)=-3/2 x-5=9/4 x=9/4 +5 x=29/4
3 sqrt -5 = 3 x 5i = 15i; 3 sqrt 9 = 3 x 3 = 9 so full answer is 135i where i is the sqrt of -1
3*sqrt(5)*x
'Squared' & 'Square Root; are the inverse mathemtical functions. 5 (squared) = 25 square root of '25' is 5 Mathematically this would be written as Square ; 5 x 5 = 5^(2) = 25 Square Root ; sqrt(25) = 25^(1/2) = 25^(0.5) = 5 NB THis can be exteneded to 'cubes' and 'cube roots' e.g. 3 x 3 x 3 = 3^(3) = 27 curt(27) = 27^(1/3) = 27^(0.3333.....) - 3 And fourth power and fourth root. e.g. Fourth power ; 2 x 2 x 2 x 2 = 2^(4) = 16 Fourth root = (4th)rt(16) = 16^(1/4) = 16^(0.25) = 2 It can be exteneded to the 'nth power' and the 'nth root'. Where 'n' is any number.
x = 7
You have : ----------------- 5 = ( x ) ( 3 )^1/2 x = ( 5 ) / ( 3 )^1/2 = +/- 2.887 <-----------------------
5 - x^2 = (the square root of 5 minus x)(the square root of 5 plus x)