Question 14

What is the positive square root of $$[25+4\sqrt{39}]$$ ?

Solution

Expression : $$[25+4\sqrt{39}]$$

= $$[25+2\sqrt{4\times39}]=[25+2\sqrt{156}]$$

= $$13+12+2\sqrt{13\times12}$$

= $$(13)^2+(12)^2+2\sqrt{13\times12}$$

Now, we know that $$a^2+b^2+2ab=(a+b)^2$$

= $$(\sqrt{13}+\sqrt{12})^2$$

Thus, square root is = $$\sqrt{13}+\sqrt{12}$$

= $$\sqrt13+2\sqrt3$$

=> Ans - (A)

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