Question

Square root of 1183/2023 with steps

Answer 1

Answer:

$\displaystyle\sqrt{\frac{1183}{2023}}=\frac{13}{17}\quad \left(\mathrm{Decimal:\quad }\:0.76470\dots \right)$

Step-by-step explanation:

$\displaystyle\sqrt{\frac{1183}{2023}}$

$\black{\displaystyle\frac{1183}{2023}}$

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

$\displaystyle=\frac{169}{289}$

$\displaystyle=\sqrt{\frac{169}{289}}$

$\displaystyle\gray{\mathrm{Apply\:radical\:rule\:}\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0}$

$\displaystyle=\frac{\sqrt{169}}{\sqrt{289}}$

$\gray{\sqrt{289}=17}$

$\displaystyle=\frac{\sqrt{169}}{17}$

$\gray{\sqrt{169}=13}$

$\displaystyle=\frac{13}{17}$

Answer 2

ANSWER

$\sqrt{ \frac{1183}{2023} } \\ \\ take \: \: the \: \: common \: \: factor \: \: 7 \\ \\ \frac{7 \sqrt{169} }{7 \sqrt{289} } \\ \\ then \: \: cancel \: \: them \\ \\ \frac{ \sqrt{169} }{ \sqrt{289} } \\ \\ value \: \: of \: \: \sqrt{169} \: \: is \: \: {13} \\ \\ value \: \: of \: \: \sqrt{289} \: \: is \: \: 17 \\ \\ \frac{( { \sqrt{13}) }^{2} }{ ({ \sqrt{17}) }^{2} } \\ \\ cancel \: \: them \\ \\ \frac{13}{17}$

Hence, the answer is 13/17.