Question

Find twice the square root of decimal number 42.25.

Answer 1

Hint: Take the square root of the given decimal number 42.25. For making it easier, 42.25 can be written as $\dfrac{{4225}}{{100}}$. After taking the square root, multiply it by 2 to get the twice the square root of 42.25.

Complete step-by-step answer:
According to the question, the given decimal number is 42.25. We have to determine twice the square root of this decimal number. This means we basically have to calculate the value of $2\sqrt {42.25} $.
First we will calculate the square root of 42.25. Now, if in square root, we multiply and divide 42.25 by 100, then the decimal number 42.25 will become a fraction $\dfrac{{4225}}{{100}}$. This will make our calculation easier and it is shown below:
$
   \Rightarrow \sqrt {42.25} = \sqrt {\dfrac{{42.25 \times 100}}{{100}}} \\
   \Rightarrow \sqrt {42.25} = \sqrt {\dfrac{{4225}}{{100}}} \\
 $
On dividing 4225 by 25, the result is 169. So 4225 can be written as $25 \times 169$. Using the in the above calculation, we’ll get:
$ \Rightarrow \sqrt {42.25} = \sqrt {\dfrac{{25 \times 169}}{{100}}} $
Now we know that the square root of 25 is 5, the square root of 169 is 13 and the square root of 100 is 10. So using these results, we’ll get:
$
   \Rightarrow \sqrt {42.25} = \dfrac{{\sqrt {25} \times \sqrt {169} }}{{\sqrt {100} }} \\
   \Rightarrow \sqrt {42.25} = \dfrac{{5 \times 13}}{{10}}
 $
Simplifying it even further, we’ll get:
$
   \Rightarrow \sqrt {42.25} = \dfrac{{65}}{{10}} \\
   \Rightarrow \sqrt {42.25} = 6.5
 $
Finally, we have to determine twice the square root of 42.25 i.e. $2\sqrt {42.25} $. So multiplying by 2 in the above calculation, we’ll get:
$
   \Rightarrow 2\sqrt {42.25} = 2 \times 6.5 \\
   \Rightarrow 2\sqrt {42.25} = 13
 $

Thus twice the square root of 42.25 is 13.

Note: The square root of any positive real number is not always a rational number. Sometimes the square root of a positive real number (either integer or decimal) is an irrational number. For example, the square root of 3, 5, 7 and 11 are irrational numbers i.e. they can’t be written in rational $\dfrac{p}{q}$ form, where p and q are integers. There are many numbers like that.