Question

√(25 - 10 √(3) + 3)
(not as a decimal)

Answer 1

`\huge\boxed{√(25-10\sqrt3+3)=5-\sqrt3}`

Explanation:

`√(25-10\sqrt3+3)=(*)\\\\25=5^2\\3=(\sqrt3)^2\\10\sqrt3=(2)(5)(\sqrt3)\\\\(*)=√(5^2-(2)(5)(\sqrt3)+(\sqrt3)^2)\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=√((5-\sqrt3)^2)\\\\\text{use}\ √(a^2)=|a|\\\\=|5-\sqrt3|=5-\sqrt3\\\\^{\text{because}\ 5>\sqrt3\to5-\sqrt3>0}`