Question 14

What is the positive square root of $$[19+4\sqrt21]?$$

Solution

Expression : $$[19+4\sqrt21]?$$

= $$[19+2\sqrt{4\times21}]=[19+2\sqrt{84}]$$

= $$7+12+2\sqrt{7\times12}$$

= $$(7)^2+(12)^2+2\sqrt{7\times12}$$

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

= $$(\sqrt{7}+\sqrt{12})^2$$

Thus, square root is = $$\sqrt{7}+\sqrt{12}$$

= $$\sqrt7+2\sqrt3$$

=> Ans - (A)

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