Question

Find the product.

`(5 + 3sqrt(2))(5 - 3sqrt(2))`

Answer 1

To find the product:

`(5 + 3sqrt(2))(5 - 3sqrt(2))`

Use the identity:

(a + b)(a – b) = a² – b²

Here:

• `a = 5`
• `b = 3sqrt(2)`

Now compute:

`a^2 = 25`

`b^2 = (3sqrt(2))^2`

= 9 × 2

= 18

So, 25 – 18 = 7