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(B) To determine the nature of the number $(\sqrt{5}+3)^{2}$,we expand it using the algebraic identity $(a+b)^{2} = a^{2} + 2ab + b^{2}$.Here,$a = \sq

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irrational

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(B) To determine the nature of the number $(\sqrt{5}+3)^{2}$,we expand it using the algebraic identity $(a+b)^{2} = a^{2} + 2ab + b^{2}$.Here,$a = \sqrt{5}$ and $b = 3$.$(\sqrt{5}+3)^{2} = (\sqrt{5})^{2} + 2(\sqrt{5})(3) + (3)^{2}$$= 5 + 6\sqrt{5} + 9$$= 14 + 6\sqrt{5}$.Since $\sqrt{5}$ is an irrational number,$6\sqrt{5}$ is also irrational. The sum of a rational number $(14)$ and an irrational number $(6\sqrt{5})$ is always an irrational number.Therefore,$(\sqrt{5}+3)^{2}$ is an irrational number.

For each question,select the proper option from the four options given to make the statement true: $(\sqrt{5}+3)^{2}$ is a / an $\ldots \ldots \ldots$ number.

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