51.0k views
18 votes
(3√7 +5)^2
simplify the problem to its simplest form.

User Awesomo
by
6.9k points

2 Answers

13 votes

Answer:


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)}}

User Ivan Melnikov
by
8.5k points
0 votes

Answer:

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)

User Vladimir Ignatov
by
7.8k points

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