How do you simplify $\sqrt{36 a^{4} b^{10}}$ $sqrt(36a^4b^10)$ ?

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Answer 1 · 2018-03-02T05:05:02

$6 a^{2} b^{5}$ $6a^2b^5$

$\sqrt{36 a^{4} b^{10}}$ $sqrt(36a^4b^10)$

${(36 a^{4} b^{10})}^{\frac{1}{2}}$ $(36a^4b^10)^(1/2)$

${(36)}^{\frac{1}{2}} {(a^{4})}^{\frac{1}{2}} {(b^{10})}^{\frac{1}{2}}$ $(36)^(1/2)(a^4)^(1/2)(b^10)^(1/2)$

$\sqrt{36} a^{2} b^{5}$ $sqrt36a^2b^5$

$6 a^{2} b^{5}$ $6a^2b^5$

For your information, taking the square root and raising to the power of $\frac{1}{2}$ $1/2$ is the same thing.

For example:

$5^{2} = 25$ $5^2=25$

$\sqrt{5^{2}} = \sqrt{25}$ $sqrt(5^2)=sqrt25$

$\sqrt{5^{2}} = 5$ $sqrt(5^2)=5$

so that must mean that taking a square root is really taking it to the $\frac{1}{2}$ $1/2$ because

$5^{2 \cdot \frac{1}{2}} = 5$ $5^(2*1/2)=5$

$5^{1} = 5$ $5^1=5$

Answer 2 · 2018-03-02T05:05:33

$6 a^{2} b^{5}$ $6a^2b^5$

$\sqrt{36 a^{4} b^{10}} = \sqrt{36} \cdot \sqrt{a^{4}} \cdot \sqrt{b^{10}}$ $sqrt(36a^4b^10) = sqrt36 * sqrt(a^4) * sqrt(b^10)$

$= 6 \cdot a^{2} \cdot \sqrt{{(b^{5})}^{2}}$ $=6*a^2*sqrt((b^5)^2)$

$= 6 a^{2} \cdot b^{5}$ $=6a^2*b^5$

$= 6 a^{2} b^{5}$ $=6a^2b^5$

Thus, we have our answer.

How do you simplify √36a4b10sqrt(36a^4b^10)?