# How do you simplify sqrt(36a^4b^10)?

Mar 2, 2018

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

#### Explanation:

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

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

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

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

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

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

For example:

${5}^{2} = 25$

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

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

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

${5}^{2 \cdot \frac{1}{2}} = 5$

${5}^{1} = 5$

Mar 2, 2018

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

#### Explanation:

$\sqrt{36 {a}^{4} {b}^{10}} = \sqrt{36} \cdot \sqrt{{a}^{4}} \cdot \sqrt{{b}^{10}}$

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

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

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