Answer

Verified

405.9k+ views

**Hint:**First we will write the given number as a product of its prime factor , then we will divide the number by the lowest factor such that in the prime product of the quotient the number of each prime factor is even.

**Complete step by step solution:**

Let’s write 9408 as its product of prime factors

$9408=2\times 2\times 2\times 2\times 2\times 2\times 3\times 7\times 7$

So we can write 9408 as ${{2}^{6}}{{3}^{1}}{{7}^{2}}$

Now we can see power of 2 is 6, power 3 is 1 and power of 7 is 2. Power of 2 and 7 is even, but power of 3 is odd so if we divide 9408 by 3 we will get a square number

The quotient when we divide 9408 by 3 we will get 3136 and the square root of 3136 is equal to 56, so the smaller number is 3 , quotient is 3136 and the square root is 56.

**So, the correct answer is “Option B”.**

**Note:**While writing evaluating the prime factor of any number check the divisibility of prime numbers such as if the sum of digits in the number is divisible by 3 the number is divisible by 3. If the last digit of the number from right is 0 or 5 then the number is divisible by 5. Multiply the last digit from right by 5 then add to the remaining number if it is divisible by 7 then the number is divisible by 7.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The mountain range which stretches from Gujarat in class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths