Question

simplify 8 root 15 ÷ 2root 3​

Answer 1

Answer:

$\dfrac{8\sqrt{15}}{2\sqrt{3}}=4\sqrt{5}\quad \left(\mathrm{Decimal:\quad }\:8.94427\dots \right)$

Step-by-step explanation:

$\dfrac{8\sqrt{15}}{2\sqrt{3}}$

$\gray{\mathrm{Divide\:the\:numbers:}\:\dfrac{8}{2}=4}$

$=\dfrac{4\sqrt{15}}{\sqrt{3}}$

$\black{\mathrm{Factor}\:\sqrt{15}:}$

$\gray{\mathrm{Factor\:}15=3\cdot \:5}$

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

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

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

$=\dfrac{4\sqrt{3}\sqrt{5}}{\sqrt{3}}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:\sqrt{3}}$

$=4\sqrt{5}$