Question

(3√7 +5)^2
simplify the problem to its simplest form.

Answer 1

`88+30√(7)`

Explanation:

Given expression:

`(3√(7)+5)^2`

A binomial is a mathematical expression with two terms connected by addition or subtraction. Therefore, the given expression is the square of a binomial.

To simplify a square of a binomial, we can use the formula for squaring a binomial:

`(a+b)^2 = a^2 + 2ab + b^2`

In this case:

• 
  `a = 3√(7)`

• 
  `b=5`

Therefore:

`\begin{aligned}(3√(7)+5)^2&=(3√(7))^2+2(3√(7))(5)+(5)^2\\\\&=(3)^2(√(7))^2+2(3√(7))(5)+(5)^2\\\\&=(9)(7)+(6√(7))(5)+25\\\\&=63+30√(7)+25\\\\&=88+30√(7)\end{aligned}`

So, the given expression (3√7 + 5)² simplifies to:

`\Large\boxed{\boxed{88 + 30√(7)}}`

Answer 2

88 + 30
`√(7) \\`

Explanation:

Expand to make easier:

(3
`√(7) \\` + 5) x (3
`√(7) \\` + 5)

FOIL:

9(7) + 15 
`√(7)` + 15
`√(7)` + 25

Simplify:

63 + 30
`√(7)` + 25

88 + 30
`√(7)`