Question

Find the square root of 0.4225
(a) 0.65
(b) 6.5
(c) 0.21
(d) 0.021

Answer 1

Hint: In this question, we first need to convert the given decimal number into fraction. Then, apply the square root to both the numerator and denominator. Now, again then convert the fraction so obtained after square root into decimal again respectively to get the result.

Complete step-by-step answer:
FRACTION:
A fraction is a number representing ratio or division of two natural numbers.
We have a top number, the numerator and a bottom number, the denominator. It simply tells us how many parts of a whole we have
DECIMAL:
In algebra, a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point.
The dot in a decimal number is called a decimal point. The digits following the decimal point show a value less than one.
Decimals are based on the preceding powers of 10 . Thus, as we move from left to right, the place value of digits get divided by 10
A tenth means \[\dfrac{1}{10}\] and in decimal form it is 0.1 and hundredth means \[\dfrac{1}{100}\] which is 0.01 in decimal form.
Now, the given decimal number in the question is
\[\Rightarrow 0.4225\]
Let us now convert this into the fraction using the above mentioned conversions
\[\Rightarrow \dfrac{4225}{10000}\]
Let us now apply the square root to this number
\[\Rightarrow \sqrt{\dfrac{4225}{10000}}\]
Now, on applying the square root to the numerator and denominator respectively we get,
\[\Rightarrow \dfrac{\sqrt{{{65}^{2}}}}{\sqrt{{{100}^{2}}}}\]
Now, this can be further written in the simplified form as
\[\Rightarrow \dfrac{65}{100}\]
Now, on further converting this to the decimal form we get,
\[\Rightarrow 0.65\]
Hence, the correct option is (a).

Note: Instead of converting the given decimal number into fraction we can directly find its square root in the decimal form itself. But it will be more clear if we convert it into fraction and then apply the square root to the numerator and denominator respectively. Both the methods give the same result.
It is important to note that while finding the square root we need to express the number as a square of another number so the square root gets cancelled.