Question

Simplify
3√5-√5+√180

Answer 1

=>3underoot5 - underoot 5 + 6underoot 5

=> < easy method __ let underoot 5 be x

so

3x - x + 6x => 8 underoot 5>

Answer 2

Answer:

$3\sqrt{5}-\sqrt{5}+\sqrt{180}=8\sqrt{5}\quad \left(\mathrm{Decimal:\quad }\:17.88854\dots \right)$

Step-by-step explanation:

$3\sqrt{5}-\sqrt{5}+\sqrt{180}$

$\mathrm{Add\:similar\:elements:}\:3\sqrt{5}-\sqrt{5}=2\sqrt{5}$

$=2\sqrt{5}+\sqrt{180}$

$\sqrt{180}$

$\mathrm{Prime\:factorization\:of\:}180:\quad 2^2\cdot \:3^2\cdot \:5$

$=\sqrt{2^2\cdot \:3^2\cdot \:5}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

$=\sqrt{5}\sqrt{2^2}\sqrt{3^2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt{2^2}=2$

$=2\sqrt{5}\sqrt{3^2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt{3^2}=3$

$=2\cdot \:3\sqrt{5}$

Refine

$=6\sqrt{5}$

$=2\sqrt{5}+6\sqrt{5}$

$\mathrm{Add\:similar\:elements:}\:2\sqrt{5}+6\sqrt{5}=8\sqrt{5}$

$=8\sqrt{5}$