How do you simplify 5 plus the square root of 3 squared? (5 + √(3)) {}^(2) ​

Question

How do you simplify 5 plus the square root of 3 squared?


`(5 + √(3)) {}^(2)`
​

Answer 1

Use identity -

(a+b)² = a²+b²+2ab

(5+√3)² = 5²+(√3)² + 2(5)(√3)

= 25 + 3 + 10√3

= 28 + 10√3

= 2(14+ 5√3)

Answer 2

28 + 10√3

Explanation:

(5 + √3)^2

Applying perfect square : (a+b)^2 = a^2 + 2ab + b^2

So in this case, it will be:

= 5^2 + 2(5)(√3) +(√3)^2

= 25 + 10√3 + 3

= 28 + 10√3