Given :

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWcaaWdaeaapeGaaGioaiabgUcaRiaaikdacqGHAiI1caaIZaaa % paqaa8qacaaIZaWaaOaaa8aabaWdbiaaiodaaSqabaGccqGHRaWkca % aI1aGaaiiOaaaaaaa!3FA0! \frac{{8 + 2\surd 3}}{{3√ 3 + 5\;}}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWcaaWdaeaapeGaaGioaiabgUcaRiaaikdacqGHAiI1caaIZaaa % paqaa8qacaaIZaWaaOaaa8aabaWdbiaaiodaaSqabaGccqGHRaWkca % aI1aGaaiiOaaaaaaa!3FA0! \frac{{8 + 2\surd 3}}{{3\sqrt 3 + 5\;}}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWcaaWdaeaapeGaaGioaiabgUcaRiaaikdacqGHAiI1caaIZaaa % paqaa8qacaaIZaWaaOaaa8aabaWdbiaaiodaaSqabaGccqGHRaWkca % aI1aGaaiiOaaaaaaa!3FA0! \frac{{8 + 2\surd 3}}{{3\sqrt 3 + 5\;}}\) = a√3 - b 

Calculations :

\(\frac {8 + 2\sqrt 3}{3\sqrt 3 + 5}\) multiply numerator and denominator by \(\frac {3\sqrt 3 - 5}{3\sqrt 3 - 5} \)

We get ⇒ 7√3 - 11 = a√3 - b 

Now compare both sides of the equation 

we will get, a = 7 and b = 11 

a + b = 7 +11 

⇒ 18 

∴ the value of a + b will be 18