What is the square root of a^2\b^5?

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Answer 1 · 2018-05-30T19:28:01

$= \frac{a \sqrt{b}}{b^{3}}$ $=(asqrtb)/(b^3)$

I assume you meant:

$= \sqrt{\frac{a^{2}}{b^{5}}}$ $=sqrt(a^2/b^5)$

$= \frac{\sqrt{a^{2}}}{\sqrt{b^{5}}}$ $=sqrt(a^2)/sqrt(b^5)$

$= \frac{a}{b^{2} \sqrt{b}}$ $=a/(b^2sqrt(b))$

now you need to rationalize the denominator by multiplying the expression by:

$\frac{\sqrt{b}}{\sqrt{b}}$ $sqrtb/sqrtb$

$= \frac{a}{b^{2} \sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}}$ $=a/(b^2sqrt(b))*sqrtb/sqrtb$

$= \frac{a \sqrt{b}}{b^{2} \cdot b}$ $=(asqrtb)/(b^2*b)$

$= \frac{a \sqrt{b}}{b^{3}}$ $=(asqrtb)/(b^3)$

Answer 2 · 2018-05-30T19:34:04

$\frac{a \sqrt{b}}{b^{3}}$ $(a sqrt b)/b^3$

$\sqrt{\frac{a^{2}}{b^{5}}}$ $sqrt(a^2/b^5)$

$:.=sqrt (a^2)/sqrt (b^5)$

$:.=(sqrt (a*a))/sqrt (b*b*b*b*b)$

$:.sqrt (a)*sqrt (a)=a$

$:.sqrt (b)*sqrt (b)=b$

$:.=a/(b^2 sqrt b) xx(b^2sqrtb)/(b^2sqrtb)$

$:.=(ab^2 sqrt b)/b^5$

$:.=(a sqrt b)/b^(5-2)$

$:.=(a sqrt b)/b^3$