Question

√245 .√45 / √75 . √ 27

Answer 1

`\sf (7)/(3)`

Explanation:

Prime factorize each irrational number and simplify it.

`\sf √(245)= √(5*7*7)=7*√(5)\\\\√(45)=√(5*3*3)=3√(5)\\\\√(75)= √(5*5*3)=5√(3)\\\\√(27)=√(3*3*3)=3√(3)`

When we multiply an irrational number by the same irrational number, we get a rational number. So, √3 *√3 = 3 and √5*√5 =5

`\sf (√(245)*√(45))/(√(75)*√(27))} =(7√(5)*3√(5))/(5√(3)*3√(3))`

`\sf = (7*3*√(5*5))/(5*3*√(3*3))\\\\\\=(7*3*5)/(5*3*3)\\\\=(7)/(3)`

Answer:

`\sf (7)/(3)`