Question

If m = 11 + 6 * sqrt 2, then find the value of ( sqrt m + sqrt 2 )raised to power ½.​

Answer 1

Answer:

=1+√2

Since m=11+6√2

m=9+2+6√2

m={3²+(√2)²+3.√2.2}

m=(a²+b²+2ab)=(a+b)²

m=(3+√2)² - eqn @

Given to find(√m+√2)½

From eqn@ √m=±(3+√2)

considering √m=(3+√2)

= (3+√2+√2)½

=(3+2√2)½

=(2+1+2√2)½

={ (√2)²+1²+2.√2.1) }½

since its also in (a+b)² form

={(√2+1)²}½

=(1+√2)²/²

=1+√2