Question

`(sqrt(3) + sqrt(5))(sqrt(5) - sqrt(3))` is equal to ______.

Options

• 1

• 2

• 3

• 8

Answer 1

`(sqrt(3) + sqrt(5))(sqrt(5) - sqrt(3))` is equal to 2.

Explanation:

The expression is `(sqrt(3) + sqrt(5))(sqrt(5) - sqrt(3))`.

Using the difference of squares formula (a + b)(a – b) = a² – b², let:

• `a = sqrt(5)`
• `b = sqrt(3)`

Then,`(sqrt(3) + sqrt(5))(sqrt(5) - sqrt(3))`

= `(sqrt(5))^2 - (sqrt(3))^2`

= 5 – 3

= 2

So the value is 2.