Question

Using identities evaluate $ {5.2^2} $

Answer 1

Hint: The given number is in decimal form. We can write this as a sum of an integer and a decimal number and then apply the identity for the sum of squares of two numbers to find the required value.
Identity to be used:
 $ {\left( {a + b} \right)^2} = {a^2} + {b^2} + 2ab $
Where, a and b are two numbers by the sum of which the original number is obtained.

Complete step-by-step answer:
We have to calculate the square of the number 5.2. We can use the following identity for doing so:
 $ {\left( {a + b} \right)^2} = {a^2} + {b^2} + 2ab $
Where, a and b are two numbers by the sum of which the original number is obtained.
The given number 5.2 can be written as sum of 5 and 0.2 as:
 $ 5.2 = \left( {5 + 0.2} \right) $
Its square is written as $ {\left( {5 + 0.2} \right)^2} $ .
Using the formula, the value of square can be calculated as:
\[
  {\left( {5 + 0.2} \right)^2} = {\left( 5 \right)^2} + {\left( {0.2} \right)^2} + 2 \times 5 \times 0.2 \;
   \to {\left( {5 + 0.2} \right)^2} = 25 + 0.04 + 2 \\
   \Rightarrow {\left( {5 + 0.2} \right)^2} = 27.04 \;
 \]
Therefore, the value of $ {5.2^2} $ is calculated to be equal to 27.04 using the identity for square of sum of two numbers represented as $ {5.2^2} $
So, the correct answer is “27.04”.

Note: For such numbers with decimals, we can use either sum or difference of the squares identity according to the approximation. For one decimal place, if the number after the decimal would have been greater than 5, then we would have used the difference from 6 but as it was smaller than 5, we used the sum from 5.
To remove the confusion for the number of decimal places while squaring a decimal number, remember that we double the decimal places actually present. As in 0.2, we have one number after decimal but in its square we will have two numbers after the decimal (0.04)