How many numbers lie between squares of the following numbers?
${\text{(i)}}$12 and 13
${\text{(ii)}}$25 and 26
${\text{(iii)}}$ 99 and 100
Answer
365.4k+ views
Hint:- Find squares of given numbers.
As, we know that,
Total numbers lying between two numbers a and b,
is given as \[b - a - 1\], where \[b > a\].
So, here we had to find total numbers lying between squares of two numbers.
So, solving all the parts.
${\text{(i)}}$So, a will be \[{(12)^2}\]
\[ \Rightarrow a = {(12)^2} = 144\]
And, b will be \[{(13)^2}\]
\[ \Rightarrow b = {(13)^2} = 169\]
So, total numbers lying between the squares of 12 and 13 will be,
\[ \Rightarrow b - a = 169 - 144 - 1 = 24\]
\[ \Rightarrow \]Hence, the total numbers lying between squares of 12 and 13 is 24.
${\text{(ii)}}$So, a will be \[{(25)^2}\]
\[ \Rightarrow a = {(25)^2} = 625\]
And, b will be \[{(26)^2}\]
\[ \Rightarrow b = {(26)^2} = 676\]
So, total numbers lying between the squares of 25 and 26 will be,
\[ \Rightarrow b - a = 676 - 625 - 1 = 50\]
\[ \Rightarrow \]Hence, the total numbers lying between squares of 25 and 26 is 50.
${\text{(iii)}}$So, a will be \[{(99)^2}\]
\[ \Rightarrow a = {(99)^2} = 9801\]
And, b will be\[{\text{ }}{(100)^2}\]
\[ \Rightarrow b = {(100)^2} = 10000\]
So, total numbers lying between the squares of 99 and 100 will be,
\[ \Rightarrow b - a = 10000 - 9801 - 1 = 198\]
\[ \Rightarrow \]Hence, the total numbers lying between squares of 99 and 100 is 198.
Note:- Whenever we came up with this type of problem then remember that,
for any two numbers a and b such that \[b > a\]. Total numbers lying between
them will be \[b - a - 1\]. But if the given two numbers are consecutive and we
had to find total numbers lying between their squares then we can also directly
say that numbers lying between them is \[2*a\].
As, we know that,
Total numbers lying between two numbers a and b,
is given as \[b - a - 1\], where \[b > a\].
So, here we had to find total numbers lying between squares of two numbers.
So, solving all the parts.
${\text{(i)}}$So, a will be \[{(12)^2}\]
\[ \Rightarrow a = {(12)^2} = 144\]
And, b will be \[{(13)^2}\]
\[ \Rightarrow b = {(13)^2} = 169\]
So, total numbers lying between the squares of 12 and 13 will be,
\[ \Rightarrow b - a = 169 - 144 - 1 = 24\]
\[ \Rightarrow \]Hence, the total numbers lying between squares of 12 and 13 is 24.
${\text{(ii)}}$So, a will be \[{(25)^2}\]
\[ \Rightarrow a = {(25)^2} = 625\]
And, b will be \[{(26)^2}\]
\[ \Rightarrow b = {(26)^2} = 676\]
So, total numbers lying between the squares of 25 and 26 will be,
\[ \Rightarrow b - a = 676 - 625 - 1 = 50\]
\[ \Rightarrow \]Hence, the total numbers lying between squares of 25 and 26 is 50.
${\text{(iii)}}$So, a will be \[{(99)^2}\]
\[ \Rightarrow a = {(99)^2} = 9801\]
And, b will be\[{\text{ }}{(100)^2}\]
\[ \Rightarrow b = {(100)^2} = 10000\]
So, total numbers lying between the squares of 99 and 100 will be,
\[ \Rightarrow b - a = 10000 - 9801 - 1 = 198\]
\[ \Rightarrow \]Hence, the total numbers lying between squares of 99 and 100 is 198.
Note:- Whenever we came up with this type of problem then remember that,
for any two numbers a and b such that \[b > a\]. Total numbers lying between
them will be \[b - a - 1\]. But if the given two numbers are consecutive and we
had to find total numbers lying between their squares then we can also directly
say that numbers lying between them is \[2*a\].
Last updated date: 26th Sep 2023
•
Total views: 365.4k
•
Views today: 7.65k
Recently Updated Pages
What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE
