Question

Evaluate : (√5 + √6)4 + (√5 − √6)4​

Answer 1

Given:

$(\sqrt{5} +\sqrt{6})4+(\sqrt{5}-\sqrt{6})4$

$4\sqrt{5}+4\sqrt{6}+4\sqrt{5}-4 \sqrt{6}$

$8\sqrt{5}$

Hence answer is $8\sqrt{5}.$

Answer 2

Concept

To evaluate an algebraic expression, find the expression's value when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify it using the order of operations.

Given

$(\sqrt{5}+\sqrt{6} )4+(\sqrt{5}-\sqrt{6} )4$

Find

We are asked to evaluate the given expression

Solution

$(\sqrt{5}+\sqrt{6} )4+(\sqrt{5}-\sqrt{6} )4\\=4(\sqrt{5}+\sqrt{6} +\sqrt{5}-\sqrt{6} )\\=4(\sqrt{5} +\sqrt{5} )\\=4(2\sqrt{5} )\\=8\sqrt{5}$

Hence the value of given expression is $8\sqrt{5}$