# A MINUS B WHOLE SQUARE WITH RADICALS

The formula for

(a + b)2 = a2 + 2ab + b 2

Problem 1 :

(2 - √3)2

Solution :

(2 - √3)2

Here a = 2 and b = √3

Using algebraic identities.

= (2)2 + (√3)2 - 2(2)(√3)

= 4 + 3 - 4√3

= 7 - 4√3

Problem 2 :

(5 - √2)2

Solution :

(5 - √2)2

Here a = 5 and b = √2

Using algebraic identities.

= (5)2 + (√2)2 - 2(5)(√2)

= 25 + 2 - 10√2

= 27 - 10√2

Problem 3 :

(4 - √6)2

Solution :

(4 - √6)2

Here a = 4 and b = √6

Using algebraic identities.

= (4)2 + (√6)2 - 2(4)(√6)

= 16 + 6 - 8√6

= 22 - 8√6

Problem 4 :

(5√2 - 1)2

Solution :

(5√2 - 1)2

Here a = 5√2 and b = 1

Using algebraic identities.

= (5√2)2 + (1)2 - 2(5√2)(1)

= 25(2) + 1 – 10(√2)

= 50 + 1 – 10(√2)

= 51 – 10(√2)

Problem 5 :

(3 - 2√2)2

Solution :

(3 - 2√2)2

Here a = 3 and b = 2√2

Using algebraic identities.

= (3)2 + (2√2)2 - 2(3)(2√2)

= 9 + 4(2) - 12√2

= 9 + 8 - 12√2

= 17 - 12√2

Problem 6 :

(3 - √7)2

Solution :

(3 - √7)2

Here a = 3 and b = √7

Using algebraic identities.

= (3)2 + (√7)2 - 2(3)(√7)

= 9 + 7 - 6√7

= 16 - 6√7

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