Question

If x is a positive real number and x2=2 then x3=​

Answer 1

Answer:

if x2=2 then X3= 3 because it depend on the expression.

Answer 2

Concept

If x > 0, then x is considered to be a positive real number.

The square of a real number x is given as-

$x^{2} =x\times x$

Any number's square root is the same as the original number, which is obtained by squaring the result, i.e. for a real number x, we have

$\sqrt{x\times x} =\sqrt{x^{2} } =x$

The cube of a real number x is given as-

$x^{3} =x\times x\times x$

Given

The given number $x$ is a positive real number and $x^{2} =2$.

Find

We have to find the value of $x^{3}$.

Solution

The square of a real number x is given as-

$x^{2} =x\times x$

It is given that $x^{2} =2$, therefore,

$x=\sqrt{2}$

Now, the cube of a real number x is given as-

$x^{3} =x\times x\times x$

Substituting the value of    $x=\sqrt{2}$, we get

$x^{3} =\sqrt{2} \times \sqrt{2}\times \sqrt{2}$

$x^{3} =\sqrt{2^{2} } \times \sqrt{2}$

Now, since $\sqrt{2^{2}} =2$, therefore,

$x^{3}=2\sqrt{2}$

Hence, $2\sqrt{2}$ is the required value of $x^{3}$.

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