A MINUS B WHOLE SQUARE WITH RADICALS

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