Question

5+3√2÷5-3√2=a+b√2 can anyone pls explain this to me?​

Answer 1

Given: (5 + 3√2) (5 - 3√2) = a + b√2.

To find: The value of a and b.

Answer:

(5 + 3√2) (5 - 3√2)

Rationalizing the denominator,

(5 + 3v√2)×(5 + 3√2)/(5 - 3v√2)×(5 + 3√2)

= (5 + 3v√2)²/(5)² - (3/2)²

= 25 + 30√2 + 18/25 - 18

= 43 + 30√2/7

∴ a = 43/7 and b = 30/7.