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Surds and indices Practice Questions & Answers

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What to the product of the roots of the equation $x^{2}-\sqrt{3}$=0

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What to the product of the roots of the equation $x^{2}-\sqrt{3}$=0
1). $+\sqrt{3}$
2). $\sqrt{3}i$
3). $-\sqrt{3}i$
4). $+\sqrt{3}$

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If $\left(\frac{3}{4}\right)^{3}\left(\frac{4}{3}\right)^{-7}$=\left(\frac{3}{4}\right)^{2x} , then x is :

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If $\left(\frac{3}{4}\right)^{3}\left(\frac{4}{3}\right)^{-7}$=\left(\frac{3}{4}\right)^{2x} , then x is :
1). -2
2). 2
3). 5
4). $2\frac{1}{2}$

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If a = $7-4\sqrt{3}$ , then the value of $a^{\frac{1}{2}}+a^{-\frac{1}{2}}$ is :

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If a = $7-4\sqrt{3}$ , then the value of $a^{\frac{1}{2}}+a^{-\frac{1}{2}}$ is :
1). $3\sqrt{7}$
2). 4
3). 7
4). $2\sqrt{3}$

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If $2^{x}$=$3^{y}$=$6^{z}$ , then $\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$ is equal to

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If $2^{x}$=$3^{y}$=$6^{z}$ , then $\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$ is equal to
1). 0
2). 1
3). $\frac{3}{3}$
4). $-\frac{1}{2}$

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If $3^{x+y}$=81 and $81^{x-y}$=3, then the value of x is

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If $3^{x+y}$=81 and $81^{x-y}$=3, then the value of x is
1). 42
2). $\frac{15}{8}$
3). $\frac{17}{8}$
4). 39