Question

(21^2-15^2)2/3
please help me​

Answer 1

$\left(21^2-15^2\right)^{\frac{2}{3}}=36$

$\left(21^2-15^2\right)^{\frac{2}{3}}$

$21^2=441$

$=\left(441-15^2\right)^{\frac{2}{3}}$

$15^2=225$

$=\left(441-225\right)^{\frac{2}{3}}$

$\mathrm{Subtract\:the\:numbers:}\:441-225=216$

$=216^{\frac{2}{3}}$

$\mathrm{Factor\:the\:number:\:}\:216=6^3$

$=\left(6^3\right)^{\frac{2}{3}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}$

$\left(6^3\right)^{\frac{2}{3}}=6^{3\cdot \frac{2}{3}}=6^2$

$=6^2$

$=36$

______________________________

is a is equal to 5 + 2√6

then a + 1/a =

$5+2\sqrt{6}\:+\:\frac{1}{5+2\sqrt{6}}$

$5+2\sqrt{6}+\frac{1}{5+2\sqrt{6}}=5+2\sqrt{6}+5-2\sqrt{6}\quad \left(\mathrm{Decimal:\quad }\:10\right)$

$5+2\sqrt{6}+\frac{1}{5+2\sqrt{6}}$

$=5+2\sqrt{6}+5-2\sqrt{6}$