Question

State whether true or false in the following:

`(sqrt(11) - sqrt(7))(sqrt(11) + sqrt(7)) = 4`

Answer 1

This statement is true.

Explanation:

Step 1: Recall the identity

(a – b)(a + b) = a² – b²

Here, `a = sqrt(11), b = sqrt(7)`.

Step 2: Apply the identity

`(sqrt(11) - sqrt(7))(sqrt(11) + sqrt(7))`

= `(sqrt(11))^2 - (sqrt(7))^2`

= 11 – 7

Step 3: Simplify

11 – 7 = 4

Step 4: Compare both sides

LHS = 4, RHS = 4 → Equal