Evaluate the value of ${(198)^2}$ using the identity${(a - b)^2} = {a^2} - 2ab + {b^2}$.
Last updated date: 30th Mar 2023
•
Total views: 308.7k
•
Views today: 2.85k
Answer
308.7k+ views
Hint: Here we go through by writing the term 198 as (200-2) because in the question we have to write in the two terms. So for solving this always think of the two numbers whose square we find easily.
Here we write 198 as (200-2)
And in the question the given identity is ${(a - b)^2} = {a^2} - 2ab + {b^2}$
We have to evaluate our number using this identity.
So we can say (200-2) is the same as (a-b) so we simply put a as 200 and b as 2 in the given identity to evaluate.
By putting the values we get,
${\left( {200 - 2} \right)^2} = {200^2} - 2 \times 200 \times 2 + {2^2}$
Now simplify the term that is on the right hand side,
i.e. R.H.S= ${200^2} - 2 \times 200 \times 2 + {2^2}$
=40000-800+4
=39196
Hence we get the answer by the help of identities that are given in the question.
For cross checking you simply find the square of 198 i.e. $198 \times 198 = 39196$ which also gives the same answer.
Note: Whenever we face such a type of question the key concept for solving the question is always think of the number in that way whose square you easily find. Here in this question the simple way is (200-2) you can also choose different numbers such as (202-4) for the identities, but in this case for finding the square of 202 is little bit complex as finding the square of 200. So always choose a simple number to prove the identities.
Here we write 198 as (200-2)
And in the question the given identity is ${(a - b)^2} = {a^2} - 2ab + {b^2}$
We have to evaluate our number using this identity.
So we can say (200-2) is the same as (a-b) so we simply put a as 200 and b as 2 in the given identity to evaluate.
By putting the values we get,
${\left( {200 - 2} \right)^2} = {200^2} - 2 \times 200 \times 2 + {2^2}$
Now simplify the term that is on the right hand side,
i.e. R.H.S= ${200^2} - 2 \times 200 \times 2 + {2^2}$
=40000-800+4
=39196
Hence we get the answer by the help of identities that are given in the question.
For cross checking you simply find the square of 198 i.e. $198 \times 198 = 39196$ which also gives the same answer.
Note: Whenever we face such a type of question the key concept for solving the question is always think of the number in that way whose square you easily find. Here in this question the simple way is (200-2) you can also choose different numbers such as (202-4) for the identities, but in this case for finding the square of 202 is little bit complex as finding the square of 200. So always choose a simple number to prove the identities.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
