# What is the square roots of 0.0004?

Jun 6, 2018

$0.02$

#### Explanation:

It can help to write the number in scientific notation:

$0.0004 = 4 \cdot {10}^{-} 4$

The square root of a product is the product of the square roots:

$\sqrt{4 \cdot {10}^{-} 4} = \sqrt{4} \cdot \sqrt{{10}^{- 4}}$

Now, $\sqrt{4}$ is easily $2$. As for the exponential part, taking the square root is the same as giving exponent $\frac{1}{2}$:

$\sqrt{{10}^{- 4}} = {\left({10}^{- 4}\right)}^{\frac{1}{2}}$

Now use the property ${\left({a}^{b}\right)}^{c} = {a}^{b c}$ to get

${\left({10}^{- 4}\right)}^{\frac{1}{2}} = {10}^{- \frac{4}{2}} = {10}^{- 2}$

So, the answer is $2 \cdot {10}^{- 2}$, or if you prefer $0.02$

Jun 6, 2018

$\pm 0.02$

#### Explanation:

$\text{note that } 100 \times 100 = 10000$

$\text{and } \left(- 100\right) \times \left(- 100\right) = 10000$

$0.0004 = \frac{4}{10000}$

$\Rightarrow \sqrt{0.0004} = \sqrt{\frac{4}{10000}} = \pm \frac{2}{100} = \pm 0.02$

Jun 6, 2018

$\sqrt{0.0004} = 0.02$

#### Explanation:

To find the square root of a number:

• group the digits into pairs, starting from the decimal point.

• The number of pairs is the same as the number of place holders in the square root.

• find the square root

$\sqrt{100} = \sqrt{\left(\textcolor{b l u e}{1} \text{ } \textcolor{g r e e n}{00}\right)} = \textcolor{b l u e}{1} \textcolor{g r e e n}{0} = 10$

sqrt16900 = sqrt(color(blue)(1)color(green)(69)" "color(red)(00)) = color(blue)(1)color(green)(3)" "color(red)(0) = 130

sqrt0.000001= sqrt(0color(blue)(.00)" "color(green)(00)" "color(red)(01)) = 0color(blue)(.0)" "color(green)(0)" "color(red)(1) = 0.001

sqrt0.0004 = sqrt(0color(blue)(.00)" "color(green)(04)) = 0color(blue)(.0)" "color(green)(2) =0.02