Question

Write whether 6√45+4√20+√405/√1050 give rational or irrational number

Answer 1

RATIONAL NUMBERS: the numbers which can be expressed in the form of p/ q where p and q are integers and q≠0, are known as rational numbers.
IRRATIONAL NUMBERS: A number whose decimal expansion is non-terminating, non-recurring is known irrational number.

SOLUTION:
6√45 +4√20 + √405/ √1050
6√9×5 +4√4×5 + √81×5 / √25×42
6×3√5 + 4×2√5+ 9√5 / 5√42
18√5 + 8√5 +9√5 / 5√42
(18+8+9)√5 / 5√42
35√5 / 5√42
7√5/√42
It gives an IRRATIONAL NUMBER

HOPE THIS WILL HELP YOU...

Answer 2

6√45 +4√20 + √405/ √1050

6√9×5 +4√4×5 + √81×5 / √25×42

6×3√5 + 4×2√5+ 9√5 / 5√42

18√5 + 8√5 +9√5 / 5√42

(18+8+9)√5 / 5√42

35√5 / 5√42

7√5/√42

It gives an IRRATIONAL NUMBER