Question

Evaluate ( root 5 + root 2 ) ^ 2 - ( root 8 - root 3 ) ^ 2

Answer 1

Answer:

Step-1 Multiplying equation’s Nr and Dr by 2+3–√−−−−−−√.

Step-2 Solving further

Step-3 Multiplying equations’s Nr andDr by [2−3–√]

Step-4 Solving further

Answer = 23[12+63–√−4+23–√−−−−−−−√]

Step-by-step explanation:

Answer 2

Answer:

(√5 + √2)^2 - (√8 - √3)^2 = -4 + 2√10 + 2√24 = -2(2 - √10 - √24)

Step-by-step explanation:

Given,

(√5 + √2)^2 - (√8 - √3)^2

We know that,

x^2 - y^2 = (x + y)(x - y)

Then, by applying the property, we get,

(√5 + √2)^2 - (√8 - √3)^2 =

= (√5 + √2 + √8 - √3)(√5 + √2 - √8 + √3)

= 5 + √10 - √40 + √15 + √10 + 2 - √16 + √6 + √40 + √16 - 8 + √24 - √15 - √6 + √24 - 3

= 7 - 11 + 2√10 + 2√24

= -4 + 2√10 + 2√24

= -2(2 - √10 - √24)

Hence,

(√5 + √2)^2 - (√8 - √3)^2 = -4 + 2√10 + 2√24 = -2(2 - √10 - √24)