The geometric mean of two surds is 5+ 373. If one of the surds is 7 + 413, then the square root of the other
surd is
Sel

2 thoughts on “The geometric mean of two surds is 5+ 373. If one of the surds is 7 + 413, then the square root of the other<br />surd is<br />Sel”

1. Answer:

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2. Given : The geometric mean of two surds is 5+ 3√3. one of the surds is 7 + 4√3,

   To find : the square root of the other surd

   O a. √3-1

   O b.4-2√3

   O 0.4 +2√3

   O d. √3+ 1​

   Solution:

   Let say other surd is X

   Then X * ( 7 + 4√3) = ( 5 + 3√3)²

   => X = ( 5 + 3√3)² / ( 7 + 4√3)

   Rationalizing denominator

   => X = ( 5 + 3√3)²( 7 -4√3) / ( 7 + 4√3)( 7 – 4√3)

   ( 7 + 4√3)( 7 – 4√3) = 49 – 48 = 1

   => X = ( 5 + 3√3)²( 7 -4√3)

   => X = ( 52 + 30√3) ( 7 -4√3)

   => X = 364 – 208√3 + 210√3 – 360

   => X = 4 + 2√3

   => X = 3 + 1 + 2√3

   => X = (√3)² + 1² + 2√3

   => X = (√3 + 1)²

   => √X = √3 + 1

   square root of the other surd = √3 + 1

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