Found 225 Articles for Class 8

Given:(i) $4x = (52)^2 – (48)^2$  (ii) $14x = (47)^2 – (33)^2$  (iii) $5x = (50)^2 – (40)^2$To do:We have to find the value of $x$ in each case.Solution:Here, we have to find the value of $x$ in each expression. The given expressions are the difference of two squares. So, to find the value of $x$ we can simplify the RHS in each case using the identity:$(a – b) (a + b) = a^2 – b^2$.Therefore, (i) $4x = (52)^2 – (48)^2$ This implies, $4x=(52+48)\times(52-48)$$4x=100\times4$$4x=400$$x=\frac{400}{4}$$x=100$Hence, the value of $x$ is $100$.(ii) $14x = (47)^2 – (33)^2$ This implies, $14x=(47+33)\times(47-33)$$14x=80\times14$$x=\frac{80\times14}{14}$$x=80$Hence, the value of $x$ ... Read More

Given:(i) $(82)^2 – (18)^2$  (ii) $(467)^2 – (33)^2$  (iii) $(79)^2 – (69)^2$  (iv) $197 \times 203$  (v) $113 \times 87$  (vi) $95 \times 105$  (vii) $1.8 \times 2.2$  (viii) $9.8 \times 10.2$To do:We have to simplify the given expressions using the formula: $(a – b) (a + b) = a^2 – b^2$Solution:Here, we have to simplify the given expressions using the formula $(a – b) (a + b) = a^2 – b^2$. The given expressions can be written as the difference of two squares by writing the terms as the sum or difference of two suitable numbers.  (i) The given expression is $(82)^2 – ... Read More

Given:(i) $\frac{((58)^2 – (42)^2)}{16}$  (ii) $178 \times 178 – 22 \times 22$  (iii) $\frac{(198 \times 198 – 102 \times 102)}{96}$  (iv) $1.73 \times 1.73 – 0.27 \times 0.27$  (v) $\frac{(8.63 \times 8.63 – 1.37 \times 1.37)}{0.726}$To do:We have to simplify the given expressions using suitable identities.Solution:Here, we have to simplify the given expressions. The given expressions(numerators in the expressions) are in the form of difference of two square numbers. We can simplify the given expressions by using the identity $a^2-b^2=(a+b) \times (a-b)$.(i) The given expression is $\frac{((58)^2 – (42)^2)}{16}$ Here, $a=58$ and $b=42$Therefore, $\frac{((58)^2 – (42)^2)}{16}=\frac{(58+42) \times (58-42)}{16}$$\frac{((58)^2 – (42)^2)}{16}=\frac{100\times16}{16}$$\frac{((58)^2 – (42)^2)}{16}=100$Hence, ... Read More

To do:We have to evaluate the given expressions using the formula for squaring a binomial.Solution:Here, we have to find the squares of some large numbers. We can find the squares of multiples of $10^n$ easily. So, express the given numbers as the sum of multiples of $10^n$ and other numbers. We can then find the squares of the given numbers by expanding the squares using the algebraic expressions:$(a+b)^2 = a^2+2ab+b^2$$(a-b)^2 = a^2-2ab+b^2$(i) The given expression is $(102)^2$.$102$ can be written as $100+2$We know that, $(a+b)^2 = a^2+2ab+b^2$Here, $a=100$ and $b=2$Therefore, $(100+2)^2=(100)^2+2\times100\times2+2^2$$(100+2)^2=10000+400+4$$(100+2)^2=10404$Hence, $(102)^2=10404$.(ii) The given expression is $(99)^2$.$99$ can be written as $100-1$We know ... Read More

Chapter Summary The Treasure Within is a good story written by Nissim Ezekiel. This story is mainly based on a conversation that happens between Ms Bela Raja and Hafeez Contractor. Here Ms Bela Raja is referred to as the editor of Sparsh and is a newsletter. On the other hand, Hafeez Contractor was one of the greatest architects in the place of India. Mr Hafeez Contractor was inferior in studies and he had an inclination towards sports. The quality of his study makes him punished by the teachers and the reason for this is that he was the gang leader ... Read More

Chapter Summary “The Selfish Giant” is a story of a giant named “Cornish Ogre”. and children playing in his garden and it was written by “Oscar Wilde”. The story delivers the need for love and the consequence of selfishness. The involvement of a young boy sent the message of God to the selfish giant. The story started with a beautiful garden where kids came to play every afternoon. The garden was gigantic, full of “soft grass” and other beautiful “fruit trees”. Birds came to the garden and sang sitting on the trees. The involvement of children enhanced the beauty of ... Read More

Chapter Summary Framton Nuttel was suffering from a nerve disorder and to get rid of it he shifted to a new town, where his sister lives. In the urge of helping his brother, she arranged a meeting with Mrs. Sappleton, who is their family friend. After reaching their house, Framton Nuttel meets with a young girl, named Vera, who is the niece of Mrs. Sappleton. As she was away for some reason, Vera starts small talks with Framton. She described a tragic story about an open window of the house. She told him that. Her aunt’s husband and two brothers ... Read More

Chapter Summary “The Fight” is a short story about two boys from various states. The story is written by Ruskin Bond, where at the end of the fight, the hate between them transformed to love. One of him was Ranji who was a Rajput and another boy is Suraj who is a Punjabi. Ranji shifts his city and moves to a new place and in the new place; he discovers a pool inside a forest. The fine water of the pool attracts Ranji and he starts swimming. The next day while swimming, Ranji meets Suraj in the pool and ... Read More

Chapter Summary ‘The Comet — II’ is a story and it is a continuation of the story of Comet- I. This story describes how the leading scientists around the world have gathered for the purpose of a conference. The experts from different parts of the world gathered together for avoiding the collision of Comet Dutta which is happening on Earth. It is seen that the Dutta Comet or Comet Dutta’s inventor was Manoj Duttada. Here, John shows a decision to organise a meeting of the experts which will be kept secret. The experts here belong to different fields. Here ... Read More

Chapter Summary ‘The Comet – I’ refers to a story that mainly revolves around the revelation of a particular comet. The discovery of this comet mainly occurs by the author Manoj Duttada. The author is very ambitious but he is an amateur astronomer who has discovered a comet first time. He creates the telescope namely Dibya Chakshu means the Divine eye. He spends most of his free time watching through a telescope. His wife is Indrani Debi and she wishes that the discovery did not occur ever. This is because of her superstitious nature. Duttada always tried to console ... Read More