To find square root of surd like this : $a+\sqrt{b}+\sqrt{c}+\sqrt{d} $ We put it equal to $\sqrt{x}+\sqrt{y}+\sqrt{z}$
To find the square root of : $21-4\sqrt{5}+8\sqrt{3}-4\sqrt{15} $ can we put this equal to $ \sqrt{x}+\sqrt{y}+\sqrt{z}$ please guide...
Note that $$(a+b\sqrt 3+c\sqrt 5+d\sqrt {15})^2\\=(a^2+3b^2+5c^2+15d^2)+(2ab+10cd)\sqrt3+(2ac+10bd)\sqrt 5 +(2ad+2bc)\sqrt{15}.$$