Question

$3\sqrt{132651}$ = ..........................

Answer 1

Answer:

$\blue{3\sqrt{132651}=153\sqrt{51}\quad \left(\mathrm{Decimal:\quad }\:1092.63855\dots \right)}$

Step-by-step explanation:

$3\sqrt{132651}$

$\sqrt{132651}$

$\gray{\mathrm{Prime\:factorization\:of\:}132651:\quad 3^3\cdot \:17^3}$

$=\sqrt{3^3\cdot \:17^3}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^b\cdot \:a^c}$

$=\sqrt{3^2\cdot \:17^2\cdot \:3\cdot \:17}$

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

$=\sqrt{3^2}\sqrt{17^2}\sqrt{3\cdot \:17}$

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

$\gray{\sqrt{3^2}=3}$

$=3\sqrt{17^2}\sqrt{3\cdot \:17}$

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

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

$=3\cdot \:17\sqrt{3\cdot \:17}$

$\gray{\mathrm{Refine}}$

$=51\sqrt{51}$

$=3\cdot \:51\sqrt{51}$

$\gray{\mathrm{Multiply\:the\:numbers:}\:3\cdot \:51=153}$

$=153\sqrt{51}$