Question

Find the square of the following numbers.
(i) $ 32 $
(ii) $ 35 $
(iii) $ 86 $
(iv) $ 93 $
(v) $ 71 $
(vi) $ 46 $

Answer 1

Hint: First we will mention the term square of a number. Then evaluate the square of the number. For evaluating the square of the term, we will be using the formula $ {a^2} + 2 \times a \times b + {b^2} $ . Break the given term and substitute the terms in the formula to evaluate the square.

Complete step by step solution:
i.We will start off by explaining the term square of a term.
So, to square a number means to just multiply it by itself.
Now we will evaluate the square of the number.
 $
   = {32^2} \\
   = {(30 + 2)^2} \\
   = {30^2} + 2 \times 30 \times 2 + {2^2} \\
   = 900 + 120 + 4 \\
   = 1024 \;
  $
Hence, the square of $ 32 $ is $ 1024 $ .

ii.We will start off by explaining the term square of a term.
So, to square a number means to just multiply it by itself.
Now we will evaluate the square of the number.
 $
   = {35^2} \\
   = {(30 + 5)^2} \\
   = {30^2} + 2 \times 30 \times 5 + {5^2} \\
   = 900 + 300 + 25 \\
   = 1225 \;
  $
Hence, the square of $ 35 $ is $ 1225 $ .

iii.We will start off by explaining the term square of a term.
So, to square a number means to just multiply it by itself.
Now we will evaluate the square of the number.
 $
   = {86^2} \\
   = {(80 + 6)^2} \\
   = {80^2} + 2 \times 80 \times 6 + {6^2} \\
   = 6400 + 960 + 36 \\
   = 7396 \;
  $
Hence, the square of $ 86 $ is $ 7396 $ .

iv.We will start off by explaining the term square of a term.
So, to square a number means to just multiply it by itself.
Now we will evaluate the square of the number.
 $
   = {93^2} \\
   = {(90 + 3)^2} \\
   = {90^2} + 2 \times 90 \times 3 + {3^2} \\
   = 8100 + 540 + 9 \\
   = 8649 \;
  $
Hence, the square of $ 93 $ is $ 8649 $ .

v. We will start off by explaining the term square of a term.
So, to square a number means to just multiply it by itself.
Now we will evaluate the square of the number.
 $
   = {71^2} \\
   = {(70 + 1)^2} \\
   = {70^2} + 2 \times 70 \times 1 + {1^2} \\
   = 4900 + 140 + 1 \\
   = 5041 \;
  $
Hence, the square of $ 71 $ is $ 5041 $ .

vi.We will start off by explaining the term square of a term.
So, to square a number means to just multiply it by itself.
Now we will evaluate the square of the number.
 $
   = {46^2} \\
   = {(40 + 6)^2} \\
   = {40^2} + 2 \times 40 \times 6 + {6^2} \\
   = 1600 + 480 + 36 \\
   = 2116 \;
  $
Hence, the square of $ 46 $ is $ 2116 $ .

Note: Substitute values along with their respective signs. While applying the formula, choose the operation according to the order of the rule. Use the PEMDAS rule here, to evaluate the value of the square of the term.