Question

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
Select one:
O a. √3-1
O b.4-2√3
O 0.4 +2√3
O d. √3+ 1​

Answer 1

Answer:

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Answer 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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