Question

Simplify and give answer √62×28

Answer 1

Answer:

$\sqrt{62\times \:28}=2\sqrt{434}\quad \left(\mathrm{Decimal:\quad }\:41.66533\dots \right)$

Step-by-step explanation:

$\sqrt{62\times \:28}$

$\gray{\mathrm{Multiply\:the\:numbers:}\:62\times \:28=1736}$

$=\sqrt{1736}$

$\gray{\mathrm{Prime\:factorization\:of\:}1736:\quad 2^3\times \:7\times \:31}$

$=\sqrt{2^3\times \:7\times \:31}$

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

$=\sqrt{2^2\times \:2\times \:7\times \:31}$

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

$=\sqrt{2^2}\sqrt{2\times \:7\times \:31}$

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

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

$=2\sqrt{2\times \:7\times \:31}$

$\gray{\mathrm{Refine}}$

$=2\sqrt{434}$