Question

State whether true or false in the following:

`sqrt(49 - 5) = 7 - sqrt(5)`

Answer 1

This statement is false.

Explanation:

Step 1: Simplify the left-hand side (LHS)

`sqrt(49 - 5) = sqrt(44)`

This does not simplify to `7 - sqrt(5)`.

It can only be expressed as `sqrt(44) = 2sqrt(11)`.

Step 2: Simplify the right-hand side (RHS)

`7 - sqrt(5)`

This is in a completely different form and cannot equal `2sqrt(11)`.

Step 3: Compare both sides

LHS = `2sqrt(11)`

RHS = `7 - sqrt(5)`

Clearly, they are not equal.