Question

Find the square root of

​

Answer 1

Answer:

$\sqrt{84\dfrac{37}{121}}=9\dfrac{2}{11}\quad \left(\mathrm{Decimal:\quad }\:9.18182\dots \right)$

Step-by-step explanation:

$\sqrt{84\dfrac{37}{121}}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}$

$\sqrt{84\dfrac{37}{121}}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\dfrac{b}{c}=\dfrac{a\cdot \:c+b}{c}$

$84\dfrac{37}{121}=\dfrac{84\cdot 121+37}{121}=\dfrac{10201}{121}$

$\sqrt{\dfrac{10201}{121}}$

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

$=\dfrac{\sqrt{10201}}{\sqrt{121}}$

$\textrm{We know that }\sqrt{121}=11\textrm{, and,}\sqrt{10201}=101$

$=\dfrac{101}{11}$

$\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}$

$\dfrac{101}{11}=9\quad \mathrm{Remainder}\quad \:2$

$\mathrm{Convert\:to\:mixed\:number:\:Quotient\dfrac{Remainder}{Divisor}}$

$\dfrac{101}{11}=9\dfrac{2}{11}$

$=9\dfrac{2}{11}$