find the square root of√2023 by division method
please write in this process
Answers
Step-by-step explanation:
Answer:
\displaystyle\sqrt{\frac{1183}{2023}}=\frac{13}{17}\quad (\mathrm{Decimal:\quad }\:0.76470\dots )
2023
1183
=
17
13
(Decimal:0.76470…)
Step-by-step explanation:
\displaystyle\sqrt{\frac{1183}{2023}}
2023
1183
\black{\displaystyle\frac{1183}{2023}}\black
2023
1183
\gray{\mathrm{Cancel\:the\:common\:factor:}\:7}Cancelthecommonfactor:7
\displaystyle=\frac{169}{289}=
289
169
\displaystyle=\sqrt{\frac{169}{289}}=
289
169
\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}Applyradicalrule
n
b
a
=
n
b
n
a
,assuminga≥0,b≥0
\displaystyle=\frac{\sqrt{169}}{\sqrt{289}}=
289
169
\gray{\sqrt{289}=17}
289
=17
\displaystyle=\frac{\sqrt{169}}{17}=
17
169
\gray{\sqrt{169}=13}
169
=13
\displaystyle=\frac{13}{17}=
17
13