If s-0 and - r - s -s- what is r in terms of s-

The correct option is E s ^ 3 given that #160; √(rs) = s #160; #160;where s gt;0 squaring both sides ⇒rs = s^2 #160; ⇒ #16 ...

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Standard XII

Mathematics

Integration of Irrational Algebraic Fractions - 1

If s>0 and ...

Question

If $s > 0$ and $\sqrt{\frac{r}{s}} = s$ , what is r in terms of s?

\frac{1}{s}

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\sqrt{s}

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s \sqrt{s}

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s^{3}

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None of the above

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Solution

The correct option is E $s^{3}$
given that

$\sqrt{\frac{r}{s}} = s$ where $s > 0$

squaring both sides

$\Rightarrow \frac{r}{s} = s^{2}$

$\Rightarrow r = s^{2} \times s$

$\Rightarrow r = s^{3}$

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If s>0 and √rs=s, what is r in terms of s?

The correct option is E s3given that √rs=s where s>0squaring both sides⇒rs=s2 ⇒r=s2×s ⇒r=s3

If $s > 0$ and $\sqrt{\frac{r}{s}} = s$ , what is r in terms of s?

The correct option is E $s^{3}$
given that

$\sqrt{\frac{r}{s}} = s$ where $s > 0$

squaring both sides

$\Rightarrow \frac{r}{s} = s^{2}$

$\Rightarrow r = s^{2} \times s$

$\Rightarrow r = s^{3}$