Question

Which of the following is true?

Options

• `sqrt(9 + 5) = 3 + sqrt(5)`

• `sqrt(6 - 1) = 5/sqrt(5)`

• `sqrt(75)/sqrt(5) = 3`

• `(sqrt(11) - sqrt(5))(sqrt(11) - sqrt(5)) = 16`

Answer 1

`bb(sqrt(6 - 1) = 5/sqrt(5))`

Explanation:

a. `sqrt(9 + 5) = 3 + sqrt(5)`

Left-hand side: `sqrt(14) ≈ 3.74`

Right-hand side: `3 + sqrt(5) ≈ 3 + 2.236 = 5.236`

Not equal.

b. `sqrt(6 - 1) = 5/sqrt(5)`

Left-hand side: `sqrt(5) ≈ 2.236`

Right-hand side: `5/sqrt(5) = sqrt(5) ≈ 2.236`

They are equal.

c. `sqrt(75)/sqrt(5) = 3`

`sqrt(75)/sqrt(5) = sqrt(75/5) = sqrt(15) ≈ 3.87`

Not equal to 3.

d. `(sqrt(11) - sqrt(5))(sqrt(11) - sqrt(5)) = 16`

`(sqrt(11) - sqrt(5))^2 = 11 + 5 - 2sqrt(55)`

= `16 - 2sqrt(55)`

Since `2sqrt(55) ≠ 0`, it is not equal to 16.