Question

Which is greater?

`6sqrt(5)` and `5sqrt(6)`

Answer 1

Given: Compare `6sqrt(5)` and `5sqrt(6)`.

Step-wise calculation:

1. Square both expressions to compare without the square roots.

`(6sqrt(5))^2`

= 6² × 5

= 36 × 5

= 180

`(5sqrt(6))^2`

= 5² × 6

= 25 × 6

= 150

2. Since 180 > 150, it means `(6sqrt(5))^2 > (5sqrt(6))^2`.

3. Both `6sqrt(5)` and `5sqrt(6)` are positive numbers, so we can conclude `6sqrt(5) > 5sqrt(6)`.

`6sqrt(5)` is greater than `5sqrt(6)`.