Question

please do solve question number 72 and 73 it's really important for me because tomorrow is my exam and I am having conclusion in these two questions from rs aggarwal book please to solve and give me the solution is important.

Answer 1

Your Answer:-

72)

$\tt \sqrt{3-2\sqrt2}$

This can only be done if we are able to make $\tt 3-2\sqrt2$ in the form of either $\tt a^2-2ab +b^2$ or $\tt a^2+2ab +b^2$ because it is the only way to take the numbers out of the square root.

So,

$\tt \sqrt{3-2\sqrt2} \\\\ \tt Can\:\:also\:\:be\:\:written\:\:as \\\\ \tt = \sqrt{(\sqrt2)^2-2\sqrt2+(1)^2} \\\\ \tt = \sqrt{(\sqrt2)^2-2(\sqrt2)(1)+(1)^2} \\\\ \tt = \sqrt{(\sqrt2-1)^2} \\\\ \tt = \sqrt2-1$

73)

$\tt \sqrt{5+2\sqrt6}$

This can only be done if we are able to make $\tt 3-2\sqrt2$ in the form of either $\tt a^2-2ab +b^2$ or $\tt a^2+2ab +b^2$ because it is the only way to take the numbers out of the square root.

$\tt \sqrt{5+2\sqrt6} \\\\ \tt Can\:\:also\:\:be\:\:written\:\:as \\\\ \tt = \sqrt{(\sqrt2)^2+2\sqrt6+(\sqrt3)^2} \\\\ \tt = \sqrt{(\sqrt2)^2+2(\sqrt2)(\sqrt3)+(\sqrt3)^2} \\\\ \tt = \sqrt{(\sqrt2+(\sqrt3)^2} \\\\ \tt = \sqrt2+\sqrt3$