Question
If $x$ is a positive real number and $x^2 = 2,$ then $x^3 =$
✓
Answer
We have to find $x^3$ provided $x^2 = 2$ So,
By raising both sides to the power $\frac{1}{2}$
$\text{x}^{2\times\frac{1}{2}}=2^{\frac{1}{2}}$
$\text{x}^{2\times\frac{1}{2}}=\sqrt{2}$
$\text{x}=\sqrt{2}$
By substituting $\text{x}=\sqrt{2}$ in $x^3$ we get
$\text{x}^3\big(\sqrt{2}\big)^3$
$=\sqrt{2}\times\sqrt{2}\times\sqrt{2}$
$=2\sqrt{2}$
The value of $x^3$ is $2\sqrt{2}$
Hence the correct choice is $b.$
By raising both sides to the power $\frac{1}{2}$
$\text{x}^{2\times\frac{1}{2}}=2^{\frac{1}{2}}$
$\text{x}^{2\times\frac{1}{2}}=\sqrt{2}$
$\text{x}=\sqrt{2}$
By substituting $\text{x}=\sqrt{2}$ in $x^3$ we get
$\text{x}^3\big(\sqrt{2}\big)^3$
$=\sqrt{2}\times\sqrt{2}\times\sqrt{2}$
$=2\sqrt{2}$
The value of $x^3$ is $2\sqrt{2}$
Hence the correct choice is $b.$
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