Question

Find the approximate value of the square root of the following numbers, correct to \[2\] places of decimal.
\[\left( i \right)\]$ 1.45$
\[\left( {ii} \right)\]$ 3.04$

Answer 1

Hint: First we have to define what the terms we need to solve the problem are. Write $1.45$ as $145.0000$ and we use a long division method to find the approximate square root of the number up to one more that the desired number of decimal places round off the square root and hence find the square root correct up to two decimal places.
Do similar process for finding the square root of $3.04$

Complete step-by-step solution:
We follow three simple steps to find the square root of a non-perfect number.
Step1: Add a suitable number of zeros after the decimal point.
Step2: Find the approximate square root of the number up to one more than the desired number of decimal places using the long division method.
Step3: Round off the square root and hence find the value correct up to two decimal places
Applying all the steps for $1.45$
Now to find its square root and correct to two decimal places;
Hence $\sqrt {1.45} = 1.20415945$ since we need to find only up to two decimal points and thus
$\sqrt {1.45} = 1.20$ which is the required decimal function for the given problem
Also, we apply the same exact procedure for the square root of $3.04$
Now to find its square root and correct to two decimal places;
Hence $\sqrt {3.04} = 1.74355957$ since we need to find only up to two decimal points and thus
$\sqrt {3.04} = 1.74$ which is the required decimal function for the given problem
Therefore, the square roots are $\sqrt {1.45} = 1.20$and $\sqrt {3.04} = 1.74$ (correct up to two decimal points)

Note: Verification $1.20415945 \times 1.20415945 = 1.449$ which is approximately $1.45$and
$1.74355957 \times 1.74355957 = 3.036$ which is approximately $3.04$.
Hence our answer is verified to be correct. Here we have a few more methods to find the square root which are prime factorisation, Long division.