Root 2 or 2^(1/2) is an irrational number.
It is approximately 1.414214
//not sure if it is correct bool isomorphic(struct Node* root1,struct Node* root2) { if(root1 root2->value) return ( isomorphic(root1->left,root2->left) && isomorphic(root1->right,root2->right) isomorphic(root1->right,root2->left) && isomorphic(root1->left,root2->right) ); else return false; }
using System; using System.Collections.Generic; using System.Text; namespace ConsoleApplication1 { class Program { static void Main(string[] args) { double a, b, c, dis,root1,root2,temp; Console.WriteLine("Enter the value of Cofficients "); Console.WriteLine("Enter the value of Cofficient a "); a = Convert.ToInt32(Console.ReadLine()); Console.WriteLine("Enter the value of Cofficient b"); b = Convert.ToInt32(Console.ReadLine()); Console.WriteLine("Enter the value of Cofficient c"); c = Convert.ToInt32(Console.ReadLine()); dis = b * b - 4 * a * c; Console.WriteLine("Dis is {0} ", dis); if (dis > 0) { temp = Math.Sqrt(dis); root1 = (-b + temp) / 2 * a; root2 = (-b - temp) / 2 * a; Console.WriteLine("First Root is {0} ",root1); Console.WriteLine("Second Root is {0} ",root2); } if (dis == 0) { root1 = -b / 2 * a; Console.WriteLine(" Root is {0} ", root1); } if (dis < 0) { temp = dis; root1 = -b ; root2 = 2 * a; Console.WriteLine("First Root is ({0} + ({1}i))/{2} ", root1,temp,root2); Console.WriteLine("Second Root is ({0} - ({1}i))/{2} ", root1, temp, root2); } Console.ReadLine(); } } }
No, it is not. Root2 and root 8 are each irrational. Root8 / root2 =2. 2 is not a member of the set.
You know that cosπ/4 and sinπ/4 both equal 1/root2, so multiplying them gets 1/2.
implicit double precision(a-h,o-z) write(*,*) "please provide the a,b,c coeff" read(*,*) A,B,C D=B*B-4*A*C if(D.GT.0) then root1=(-B/(2*A))+(SQRT(D))/(2*A) root2=(-B/(2*A))-(SQRT(D))/(2*A) write(*,*) root1,root2 elseif(D.EQ.0) then root1=(-B/(2*A)) root2=root1 write(*,*) root1,root2 else root1=(-B/(2*A))+(SQRT(-D))/(2*A) root2=(-B/(2*A))-(SQRT(-D))/(2*A) a=(root1+root2)/2 b=(root1-root2)/2 write(*,*) 'realpartroot=',a, 'complexpartroot=',b endif stop END
141.08596670115706443962956239886 is the root2 of 19905.25
6.25
Write three rational numbers between root2 root3 ?
Assume it's rational. Then 2 + root2 = some rational number q. Then root2 = q - 2. However, the rational numbers are well-defined under addition by (a,b) + (c,d) = (ad + bc, bd) (in other words, you can add two fractions a/b and c/d and always get another fraction of the form (ad + bc)/bd.) Therefore, q - 2 = q + (-2) is rational, since both q and -2 are rational. This implies root2 must be rational, which is a contradiction. Therefore the assumption that 2 + root2 is rational must be false.
Because they cannot be expressed as ratios of integers.
It is known that the square root of an integer is either an integer or irrational. If we square root2 root3 we get 6. The square root of 6 is irrational. Therefore, root2 root3 is irrational.
10 root2 (10 x 1.41421356) is about 14.1421356 or 14.14.