Question

Find the value of $ \sqrt {0.9} \times \sqrt {1.6} $

Answer 1

Hint: We need to convert both the values in fraction form having denominators as 10, 100, 1000 based on the place of decimal given in the question. And then finding the product of individual square root value of the given values will land you to the answer.

Complete step-by-step answer:
At first, we have to convert the value 0.9 in the form of fraction.
So, $ 0.9 = \dfrac{9}{{10}} $
Similarly, converting the value 1.6 in the form of fraction we will be getting as below
 $ 1.6 = \dfrac{{16}}{{10}} $
Now, the expression $ \sqrt {0.9} \times \sqrt {1.6} $ can be expressed as $ \sqrt {\dfrac{9}{{10}}} \times \sqrt {\dfrac{{16}}{{10}}} $
i.e.
 $ \Rightarrow \sqrt {\dfrac{9}{{10}}} \times \sqrt {\dfrac{{16}}{{10}}} = \dfrac{{\sqrt 9 }}{{\sqrt {10} }} \times \dfrac{{\sqrt {16} }}{{\sqrt {10} }} $
 $ = \dfrac{{\sqrt 9 \times \sqrt {16} }}{{\sqrt {10} \times \sqrt {10} }} $
 $ = \dfrac{{\sqrt 9 \times \sqrt {16} }}{{{{(\sqrt {10} )}^2}}} $
\[ = \dfrac{{3 \times 4}}{{10}}\]
\[ = \dfrac{{12}}{{10}}\]
\[ = 1.2\]
Hence, the value of $ \sqrt {0.9} \times \sqrt {1.6} $ is 1.2.

Additional Information: We can also solve the above equation in another way also. In that case we just need to multiply the two values and then need to find out the square root of the product. For example, the product of $ \sqrt {0.9} \times \sqrt {1.6} $ will be $ \sqrt {1.44} $ which stands to 1.2. But this method is suitable only when the values are small and the decimal place may also create confusion. So, I prefer the first method over this one.

Note: Kindly don’t confuse while converting the values to fraction and again reconverting them replacing the values of 10 present in the denominator. And also you may go for any of the two methods but in both the cases keep in mind while finding the square root values and putting the decimal based on the denominator obtained. Rest you can go for any of the methods based on your convenience or any availability of time.