Question

Solve This Quickly Guys.

First Question answer=√2+√3+√5

Second Question Answer=0

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Answer 1

Solution 1:-

=> 10 + 2√6 + √60 + 2√10

Breaking the EQ to make the formula of (x + y+ z)²

( x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

=> (x + y+ z)² = x² + y² + z² + 2( xy + yz + zx)

Breaking Seperately:-

10 = 5, 3, 2 = x² + y² + z²___________(1).

2√6 = 2xy

=> √6 = xy.__________________(2).

√60 = 2yz

=> 2√15 = 2yz

=> √15 = yz ___________________(3).

2√10 = 2xz

=> √10 = xz_____________________(4).

From EQ (1), (2), (3) & (4) the equation seems as the Formula of (x + y + z)²

=> ( x+y+z)² = x² + y² + z² + 2( xy + yz + zx).

Putting the values from all the above equations:

=> ( x² + y² + z²) + 2( xy + yz + zx)

=> ( √5² + √2² + √3²) + 2( √6 + √15 + √10)

=> ( √5 + √3 + √2)²

Hence,

The Positive Square Root is ( √5 , √3, √2).

Solution 2:-

Refer to the Attachment!!