Question

What is ten times the square root of the following decimal number?
7.29

Answer 1

Hint: Firstly convert the decimal into fraction and then factorise the numerator and denominator to make them into a perfect square and then multiply it by $ 10 $ to get the required answer.

Complete step-by-step answer:
From the question, the decimal number we have is 7.29 and we have to calculate the value of $ 10 \times \sqrt {7.29} $ .
First, we convert the decimal number into fraction to make the calculation simpler, we have,
 $ \dfrac{{729}}{{100}} $
We know that the 729 is the cube of 9.
Second, we factorise the numerator and the denominator and take the square root of it, we have,
\[
\Rightarrow \sqrt {\dfrac{{729}}{{100}}} = \sqrt {\dfrac{{9 \times 9 \times 9}}{{10 \times 10}}} \\
 = \sqrt {\dfrac{{\left( {3 \times 3} \right) \times \left( {3 \times 3} \right) \times \left( {3 \times 3} \right)}}{{10 \times 10}}} \\
 = \dfrac{{3 \times 3 \times 3}}{{10}}
\]
After further simplification of the above mathematical expression, we get,
 $
\Rightarrow \sqrt {7.29} = \dfrac{{27}}{{10}}\\
 = 2.7
 $
We have to find the value of ten times of $ \sqrt {7.29} $ , we get,
 $
\Rightarrow 10 \times \sqrt {7.29} = 10 \times 2.7\\
 = 27
 $
Hence, the value of ten times the square root of decimal number 7.29 is $ 27 $ .

Note: Square of a number is the multiplication of a number with itself, square root is just the opposite, it is division of a number with itself.
For any real number p and q, if the square of p is equal to q, then the square root of q is equal to p.
For example: 36 is square of 6 and the square root of 36 is 6.

To find the square root of a decimal number, we should convert them into fractional number, so that our calculation becomes easy and then factorise the numerator and denominator into the perfect square form for example: $ \sqrt {\dfrac{{49}}{{25}}} = \sqrt {\dfrac{{7 \times 7}}{{5 \times 5}}} = \dfrac{7}{5} $ .