What is the value of positive square root of $(69+$ $28 sqrt{5}$ )?

$69+28 sqrt{5}=69+2 imes 7 imes 2 sqrt{5}$

$=49+20+2 imes 7 imes 2 sqrt{5}$

$=(7)^{2}+(2 sqrt{5})^{2}+2 imes 7 imes 2 sqrt{5}=(7+2 sqrt{5})^{2}$

$herefore sqrt{69+28 sqrt{5}}=sqrt{(7+2 sqrt{5})^{2}}=7+2 sqrt{5}$