A PLUS B WHOLE SQAURE FORMULA WITH RADICALS

The formula for 

(a + b)² = a² + 2ab + b ²

Expand and simplify the following perfect squares :

Problem 1 :

(1 + √2)²

Solution :

(1 + √2)²

Using algebraic identities.

= (1)² + (√2)² + 2(1)(√2)

= 1 + 2 + 2√2

= 3 + 2√2

Problem 2 :

(√3 + 2)²

Solution :

(√3 + 2)²

Using algebraic identities.

= (√3)² + (2)² + 2(√3)(2)

= 3 + 4 + 4√3

= 7 + 4√3

Problem 3 :

(1 + √5)²

Solution :

(1 + √5)²

Using algebraic identities.

= (1)² + (√5)² + 2(1)(√5)

= 1 + 5 + 2√5

= 6 + 2√5

Problem 4 :

(1 + 3√2)²

Solution :

(1 + 3√2)²

Using algebraic identities.

= (1)² + (3√2)² + 2(1)(3√2)

= 1 + 9(2) + 6√2

= 1 + 18 + 6√2

= 19 + 6√2

Problem 5 :

(4√3 + 5)²

Solution :

(4√3 + 5)²

Using algebraic identities.

= (4√3)² + (5)² + 2(4√3)(5)

= 16(3) + 25 + 40(√3)

= 48 + 25 + 40(√3)

= 73 + 40(√3)

Problem 6 :

(2√11 + 3)²

Solution :

(2√11 + 3)²

Using algebraic identities.

= (2√11)² + (3)² + 2(2√11)(3)

= 4(11) + 9 + 12(√11)

= 44 + 9 + 12(√11)

= 53 + 12(√11)