Question

Find the square of the following numbers without actual multiplication 42.

Answer 1

Hint: Here we have to use the algebraic identity to find the square of the given number. So first, we will split the number into a sum of two numbers. Then we will square it by using the algebraic identity. We will then solve it to get the value of the square of the number.

Complete step-by-step answer:
First we have to split the given number into two numbers. Therefore, we can write the number 42 as
\[42 = 40 + 2\]
Now we will square both sides of the equation. Therefore, we get
\[ \Rightarrow {\left( {42} \right)^2} = {\left( {40 + 2} \right)^2}\]
Now using the algebraic identity i.e. \[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\], we get
\[ \Rightarrow {\left( {42} \right)^2} = {\left( {40} \right)^2} + \left( {2 \times 40 \times 2} \right) + {\left( 2 \right)^2}\]
Applying the exponent on the terms, we get
\[ \Rightarrow {\left( {42} \right)^2} = 1600 + 160 + 4\]
Adding the terms, we get
\[ \Rightarrow {\left( {42} \right)^2} = 1764\]
Hence, the square of number 42 without actual multiplication is 1764.

Note: Here we have to note that for making the square equation we should know the basic algebraic identities. Algebraic identities are equations where the value of the left-hand side of the equation is identically equal to the value of the right-hand side of the equation.
We should also know that the squaring means forming a perfect square equation.
Square of a number is defined as the product of that number twice with itself and it is represented as \[{a^2}\] . A Cube of a number is defined as the product of the number thrice with itself and it is represented as \[{a^3}\].