Answer:
[tex]\sqrt{10+4\sqrt{6 }[/tex] = 4.44948
or = [tex]\sqrt{6} + 2[/tex]
step by step...solving
10 + 4[tex]\sqrt{6}[/tex]
add/subtract [tex]\sqrt{6}[/tex]² = 6
=10 + 4[tex]\sqrt{6}[/tex] + [tex]\sqrt{6}[/tex]² - 6
Refine
= [tex]\sqrt{6}[/tex] ² + 4[tex]\sqrt{6}[/tex] + 4
rewrite ↑ as [tex]\sqrt{6}[/tex]² + 2[tex]\sqrt{6}[/tex] * 2 + 2²
apply Perfect Square Formula (a + b)² = a² + 2ab +²
a = [tex]\sqrt{6}[/tex], b=2
= ([tex]\sqrt{6}[/tex] + 2)²
= [tex]\sqrt \sqrt({6}+ 2)[/tex]2square
(the 2 square would not fit like i wanted it to)
apply radical rule [tex]\sqrt[n]{a^{n} } = a[/tex], assuming a ≥ 0
= [tex]\sqrt{6} + 2[/tex]
posting others as picture (have an account with Symbolab to help me as well. Just taking too long to type in the step by step if you need it. all pictures have the decimal result.
