Ex.6.2 Q1 Squares and Square Roots Solutions - NCERT Maths Class 8

Go back to  'Ex.6.2'

Question

Find the squares of the following numbers.

   (i) \(32\)   

  (ii) \(35\) 

 (iii) \(86\)   

 (iv) \(93\)   

 (v) \(71\)   

(vi) \(46\)

Text Solution

What is known?

Numbers

What is unknown?

Squares of the numbers.

Reasoning 1:

There is a way to find this by without multiplication.

Use identity: 

\((a+b)^2=a^2+2ab+b^2\)

\((a+b)^2=a^2-2ab+b^2\)

Steps (i): 

\[\begin{align}32 &= 30 + 2\\{32^2} &= {(30 + 2)^2}\\ &= 30(30 + 2) + 2(30 + 2)\\ &= {30^2} + 30 \times 2 + 2 \times 30 + {2^2}\\ &= 900 + 60 + 60 + 4\\ &= 1024\end{align}\]

Reasoning 2:

If a number have its unit digit \(5\) i.e. \(a5\), its square number will be [\(a (a+1)\; \rm hundred+25\)].

Steps (ii): 

Hence \(a = 3\)

Square of the number \(35\)

\[\begin{align}&= [3(3+1) \text{hundreds}+25]\\&= [ (3\times 4) \;\text{hundreds}+25]\\&= 1200+25\\&= 1225 \end{align}\]

Reasoning:

There is a way to find this by without multiplication

Steps (iii): 

\[\begin{align}86 &= 80 + {86^2}\\ &= {(80 + 6)^2}{\rm{ }}\\ &= 80(80 + 6) + 6(80 + 6)\\ &= {80^2} + 80 \times 6 + 6 \times 80 + {6^2}\\ &= 6400 + 480 + 480 + 36\\&= 7396 \end{align}\]

Reasoning:

There is a way to find this by without multiplication.

Steps (iv):

\[\begin{align}93 &= 90 + 3\\{93^2} &= {(90 + 3)^2}\\ &= 90(90 + 3) + 3(90 + 3)\\ &= {90^2} + 90 \times 3 + 3 \times 90 + {3^2}\\ &= 8100 + 270 + 270 + 9\\ &= 8649 \end{align}\]

Reasoning

There is a way to find this by without multiplication.

Steps (v):

\[\begin{align}71 &= 70 + 1\\{71^2} &= {(70 + 1)^2}\\ &= 70(70 + 1) + 1(70 + 1)\\ &= {70^2} + 70 \times 1 + 1 \times 70 + {1^2}\\ &= 4900 + 70 + 70 + 1\\ &= 5041 \end{align}\]

Reasoning

There is a way to find this by without multiplication.

Steps (vi):

\[\begin{align} 46 &= 40 + 6\\{46^2} &= {(40 + 6)^2}\\ &= 40(40 + 6) + 6(40 + 6)\\ &= {40^2} + 40 \times 6 + 6 \times 40 + {6^2}\\ &= 1600 + 240 + 240 + 36\\ &= 2116 \end{align}\]

  
Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school