Question

$\sqrt{0.0004} =$


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Answer 1

Required Solution:

Here, as per the provided question we have to find the square root of 0.0004.

So, one thing you have to always remember while doing these type of questions is that write the number which have decimals into fraction.

Thus, we can write 0.0004 as 4/10000. That is:

$\sf { \longrightarrow \sqrt{0.0004} = \sqrt{ \dfrac{4}{1000}}}$

Now as we know that,

• ${\underline {\boxed {\large {\bf \gray { \sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}} } }}}}$

$\sf{ \longrightarrow \sqrt{\dfrac{4}{10000}} = \dfrac{\sqrt{4}}{\sqrt{10000}} }$

Now,

• √4 = 2

→ By prime factorization, we get that:–

→ √4 = √2 × 2

→ √4 = 2

Also,

• √10000 = 100

→ By prime factorization, we get that:–

→ √10000 = √10 × 10 × 10 × 10

→ √10000 = 10 × 10

→ √10000 = 100

Thus,

$\sf{ \longrightarrow \sqrt{\dfrac{4}{10000}} = \dfrac{2}{100} }$

$\sf{ \longrightarrow \sqrt{\dfrac{4}{10000}} = 0.02 }$

So, square root of 0.0004 is 0.02.

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Know More:

• ${\underline {\boxed {\large {\bf \gray { \sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}} } }}}}$

• ${\underline {\boxed {\large {\bf \gray { \sqrt{a} \times \sqrt{b} = \sqrt{ a \times b} } }}}}$

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