Question

please its very very urgent , help me find the square root of 9716​

Answer 1

Answer:

$\sqrt{9716}=2\sqrt{2429}\quad \left(\mathrm{Decimal:\quad }\:98.56977\dots \right)$

Step-by-step explanation:

$\sqrt{9716}$

$\black{\mathrm{Prime\:factorization\:of\:}9716:}$

$9716$

$\gray{9716\:\mathrm{divides\:by}\:2\quad \:9716=4858\cdot \:2}$

$=2\cdot \:4858$

$\gray{4858\:\mathrm{divides\:by}\:2\quad \:4858=2429\cdot \:2}$

$=2\cdot \:2\cdot \:2429$

$\gray{2429\:\mathrm{divides\:by}\:7\quad \:2429=347\cdot \:7}$

$=2\cdot \:2\cdot \:7\cdot \:347$

$\gray{2,\:7,\:347\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}}$

$=2\cdot \:2\cdot \:7\cdot \:347$

$=2^2\cdot \:7\cdot \:347$

$=\sqrt{2^2\cdot \:7\cdot \:347}$

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

$=\sqrt{2^2}\sqrt{7\cdot \:347}$

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

$\gray{\sqrt{2^2}=2}$

$=2\sqrt{7\cdot \:347}$

$\gray{\mathrm{Refine}}$

$=2\sqrt{2429}$