Question

5√2+3√3 and. 2√2-5√3.​

Answer 1

Step-by-step explanation:

Two easy methods to solve such questions:

By Inspection

Let the numbers be in general form “a root b”.

In “5 root 7” both “a” and “b” are greater than in “3 root 2” and “2 root 3”. So “5 root 7” is greatest.

In “3 root 2” and “2 root 3”, the two numbers are of the form “x root y” and “y root x”, respectively. So clearly, the number with greater integer as “a” will be greater, since “root t” <= “t” always.

Therefore “5 root 7” > “3 root 2” > “2 root 3”.

By Squaring

By squaring all the numbers, numbers become: 175, 18, 12

So order is 175>18>12.

Now if a^2 > b^2 > c^2, then a > b > c for all a,b,c > 0.

Therefore “5 root 7” > “3 root 2” > “2 root 3”.