Question

Evaluate √1183÷√2023​

Answer 1

Answer:

$\dfrac{\sqrt{1183}}{\sqrt{2023}}=\dfrac{13}{17}\quad \left(\mathrm{Decimal:\quad }\:0.76471\dots \right)$

Step-by-step explanation:

$\dfrac{\sqrt{1183}}{\sqrt{2023}}$

$\mathrm{Factor\:}1183=13^2\cdot \:7$

$=\sqrt{13^2\cdot \:7}$

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

$=\sqrt{7}\sqrt{13^2}$

$=13\sqrt{7}$

$\mathrm{Factor\:}2023=17^2\cdot \:7$

$=\sqrt{17^2\cdot \:7}$

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

$=\sqrt{7}\sqrt{17^2}$

$=17\sqrt{7}$

$=\dfrac{13\sqrt{7}}{17\sqrt{7}}$

$\mathrm{Cancel\:the\:common\:factor:}\:\sqrt{7}$

$=\dfrac{13}{17}$