Question

The \[\sqrt {\dfrac{{0.361}}{{0.00169}}} \] is equal to
A. \[\dfrac{{19}}{{30}}\]
B. \[\dfrac{{19}}{3}\]
C. \[\dfrac{{19}}{{13}}\]
D. \[\dfrac{{190}}{{13}}\]

Answer 1

Hint: Square root of a number is a value, which on multiplies by itself gives the original number. To find the square root of the number, figure out whether the given number is a perfect square or imperfect square and the perfect squares are the squares of the whole numbers.

Complete step by step solution:
The given expression is
\[\sqrt {\dfrac{{0.361}}{{0.00169}}} \]
Hence, multiply the numerator and denominator by \[{10^5}\]
\[\sqrt {\dfrac{{0.361 \times {{10}^5}}}{{0.00169 \times {{10}^5}}}} \]
Simplify the terms
\[\dfrac{{\sqrt {361} \times \sqrt {{{10}^2}} }}{{\sqrt {169} }}\]
\[\Rightarrow\dfrac{{19 \times 10}}{{13}}\]
\[\Rightarrow\dfrac{{190}}{{13}}\]
Therefore, the value of \[\sqrt {\dfrac{{0.361}}{{0.00169}}} \] is equal to \[\dfrac{{190}}{{13}}\].

Hence, option D is the right answer.

Additional information:
The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.Any number can be expressed as a product of prime numbers. This method of representation of a number in terms of the product of prime numbers is termed as the prime factorization method. It is the easiest method known for the manual calculation of the square root of a number.

Finding the square root of a number is the inverse operation of squaring that number.Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers. Many mathematical operations are an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on.

Note: To find the square root of any number, we need to figure out whether the given number is a perfect square or imperfect square. If the number is a perfect square, such as 1, 4, 9, 16, etc., then we can factorise the number by prime factorisation method. If the number is an imperfect square, such as 2, 3, 5, etc., then we have to use a long division method to find the root.