Question

Find the square of the following number: 35

Answer 1

Hint: Use the formulae $ {\left( {a + b} \right)^2} = {a^2} + 2a \cdot b + {b^2} $ and $ {\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2} $ .
Use the concept of breaking the numbers into simple numbers that can be easily squared and apply the formula to find the square of the numbers.

Complete step-by-step answer:
The number 35 can be broken into 30 and 5.
We know that $ 30 + 5 = 35 $ .
Let us assume that $ a = 30 $ and $ b = 5 $ .
To find the square of the sum of two numbers, variables or constants, we can use the formula $ {\left( {a + b} \right)^2} = {a^2} + 2a \cdot b + {b^2} $ .
Substitute the 30 for $ a $ and $ 5 $ for b in the formula $ {\left( {a + b} \right)^2} = {a^2} + 2a \cdot b + {b^2} $ , to find the square of 35.
 $
\Rightarrow {\left( {30 + 5} \right)^2} = {30^2} + 2\left( {30} \right) \cdot \left( 5 \right) + {5^2}\\
 = 900 + 60 \cdot 5 + 25\\
 = 900 + 300 + 25\\
 = 1225
 $

Therefore, the square of the number 35 is equal to 1225.

Additional Information:
Square and cube of a number can be found out by using a simple formula.
The square of the sum of two numbers can be calculated by adding the square of the individual numbers to twice the product of the two numbers, i.e. $ {\left( {a + b} \right)^2} = {a^2} + 2a \cdot b + {b^2} $ . This concept can be used to find the square of a number.
Also, the square of the difference between two numbers can be calculated by subtracting twice the product of the two numbers from the sum of the square of those two numbers, i.e. $ \Rightarrow {\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2} $ .
Students can use the concept of the formula
 $ \Rightarrow {a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right) $ which states that the difference between the squares of two numbers can be equal to the product of the sum and difference of the two numbers.

Note: This question can also be solved using another method. Break 35 as $ 40 - 5 $ and substitute $ a = 40,{\rm{ }}b{\rm{ = 5}} $ in $ {\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2} $ we get, $ {\left( {40 - 5} \right)^2} = {40^2} - 2\left( {40} \right)\left( 5 \right) + {5^2} $
It can be further simplified to get the value as $ 1600 - 400 + 25 = 1225 $ .