Answer
451.2k+ views
Hint: We will start by finding the largest number of 5 digits. Then we will use the fact that the number which is a perfect square has all the factors in even multiples and then find the factors of each of the options given in the question to find the greatest number which is a perfect square.
Complete step-by-step answer:
Now, we have to find the largest number of 5 digits which is a perfect square. We know the largest number of 5 digits is 99999.
Now, the prime factorization of 99999 is,
$99999={{3}^{2}}\times 271\times 41........\left( 1 \right)$
Now, we will take the next number which is less than 99999 and find its factor. So, in option (C) we have 99976
$99976=2\times 2\times 2\times 12497...........\left( 2 \right)$
Now, we have the next number which is smaller than 99999 is option (D) as 99856. Now, the prime factorization of this number is,
$\begin{align}
& 99856=2\times 2\times 2\times 2\times 79\times 79 \\
& 99856={{2}^{4}}\times {{79}^{2}}...........\left( 3 \right) \\
\end{align}$
Now, we know that for a number to be a perfect square its factors must be in even numbers as we can see from (1), (2) all the factors are not in even numbers but in (3) the factor 2 is 4 times and 79 is 2 times. Hence, all the factors are even times and therefore, we have the largest 5 digit number which is a perfect square is 99856.
Hence, the correct option is (D).
Note: To solve these questions it is important to note that we have used the fact that the number which is a perfect square has all its factors even number of times. Hence, we have the number 99856 as a perfect square because it has all the factors, even numbers of times.
Complete step-by-step answer:
Now, we have to find the largest number of 5 digits which is a perfect square. We know the largest number of 5 digits is 99999.
Now, the prime factorization of 99999 is,
$99999={{3}^{2}}\times 271\times 41........\left( 1 \right)$
Now, we will take the next number which is less than 99999 and find its factor. So, in option (C) we have 99976
$99976=2\times 2\times 2\times 12497...........\left( 2 \right)$
Now, we have the next number which is smaller than 99999 is option (D) as 99856. Now, the prime factorization of this number is,
$\begin{align}
& 99856=2\times 2\times 2\times 2\times 79\times 79 \\
& 99856={{2}^{4}}\times {{79}^{2}}...........\left( 3 \right) \\
\end{align}$
Now, we know that for a number to be a perfect square its factors must be in even numbers as we can see from (1), (2) all the factors are not in even numbers but in (3) the factor 2 is 4 times and 79 is 2 times. Hence, all the factors are even times and therefore, we have the largest 5 digit number which is a perfect square is 99856.
Hence, the correct option is (D).
Note: To solve these questions it is important to note that we have used the fact that the number which is a perfect square has all its factors even number of times. Hence, we have the number 99856 as a perfect square because it has all the factors, even numbers of times.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)