In the International Grandmaster Championship, a total of 105 games were played where each team played exactly one game with all the other teams. How many teams were participating in the Championship?

10√6 ; √5/6 ; 42√14

Step-by-step explanation:

1)  - factorise 240

240/ 2 = 120

120/2 = 60

60/2 = 30

30/2 = 15

15/3 = 5

5/5 = 1

240 = 2^4 * 3 * 5

- simplify . We can in particular simplify  by dividing the index of the radius and the exponent by 2

- factorise 12

12/2 =.6

6/2 = 3

3/3 = 1

12 = 2^2 * 3

- simplify

- divide

number : number = 4/2 = 2

square : square = √15 / √3 = √5

- multiply √30 with 2√5

number x number = 2x1 = 2

square x square = √30 x √5 = √150

2√150

- factorize 150

150/ 2 = 75

75/3 = 25

25/5 = 5

5/5 = 1

150 = 5^2 x 2 x 3

- simplify

- multiply 2 and 5

10√6

2)  remember that a division of two terms with the same square can be rewrite as

- rewrite the expression in this way

- solve the squares of the denominators

√5/3 + √5/12 -√5/4

- rewrite the fraction with the same denominator = 12

(4√5 + √5 - 3√5)/12

- simplify the numerators by sum the numbers

2√5/12

- divide 2 and 12

√5/6

3)

- multiply 3√2 and √14

number x number = 3 x 1 = 3

square x square = √2 x √14  = √28

3√28

- factorise 28

28 = 2^2 x 7

- simplify

- multiply 3 and 2

6√7

- factorise 98

98/2 = 49

49/7 = 7

7/7 = 1

98 = 7^2 * 2

- simplify

- multiply 6√7 and 7√2

number x number = 42

square x square = √14

42√14