Question : The value of $\sqrt{3\sqrt{3\sqrt{3......}}}$ is equal to:
Option 1: $\sqrt{3}$
Option 2: $3$
Option 3: $2\sqrt{3}$
Option 4: $3\sqrt{3}$
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Correct Answer: $3$
Solution : Given: $\sqrt{3\sqrt{3\sqrt{3......}}}$ Let $x = \sqrt{3\sqrt{3\sqrt{3......}}}$ $ ⇒ x = \sqrt{3x}$ By squaring both sides, we get: $ ⇒ x^{2} = 3x$ $ ⇒ x = 3$ Hence, the correct answer is $3$.
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Question : What is the value of $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}}$?
Option 1: $2\sqrt{6}$
Option 2: $4\sqrt{6}$
Option 3: $2$
Option 4: $4$
Question : The value of $(\sqrt {4^3+15^2})^3$ is:
Option 1: 4913
Option 2: 4313
Option 3: 4193
Option 4: 3943
Question : What is the value of $\sqrt{1509+\sqrt{144}}?$
Option 1: 39
Option 2: 37
Option 3: 41
Option 4: 49
Question : The longest side of the obtuse triangle is 7 cm and the other two sides of the triangle are 4 cm and 5 cm. Find the area of the triangle.
Option 1: $1 \sqrt{3} \mathrm{~cm}^2$
Option 2: $6 \sqrt{3} \mathrm{~cm}^2$
Option 3: $3 \sqrt{2} \mathrm{~cm}^2$
Option 4: $4 \sqrt{6} \mathrm{~cm}^2$
Question : The value of $\frac{2}{3}$ of $\frac{5}{8}$ of $276-\sqrt{7056}$ is:
Option 1: 36
Option 2: 31
Option 3: 33
Option 4: 29
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