Is 9408 a perfect square find the smallest number by which it should be divided to make it a perfect square also find the square root?

Solution :-

To find the smallest number by which 9408 must be divided so that the quotient is a perfect square, we have to find the prime factors of 9408.

9408 = 2*2*2*2*2*2*3*7*7

Prime factors of 9408 are 2, 2, 2, 2, 2, 2. 3, 7, 7
Out of the prime factors of 9408, only 3 is without pair.
So, 3 is the number by which 9408 must be divided to make the quotient a perfect square.

9408/3 = 3136

Square root of 3136

56
        _____________
   5   |    3136
   5   |    25
___  |______
106  |      636
   6   |      636
        |_______
        |      000

       So, √3136 = 56

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Find the smallest number by which 9408 must be divided so that the quotient is a perfect square. Find the square root of the quotient.A. Smaller number :5 Quotient : 3036 Square root :54B. Smaller number :3 Quotient :3136 square root:56C. Smaller number :7 Quotient :3236 square root:57D. Data insufficient

Answer

Verified

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.

hello friends question of Savita find the smallest number by which 9408 must be divided so that it becomes a perfect square also find the square root of the perfect square so obtained as a pahle Ham 9408 ke sare prime factors nikal lete hain Pahle Se 2020 Mein 47042 City white karne mein Milega free 523277 6E 2588 Malegaon 4-147 349 then 7087 then again 7 schedule

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Hoga Agar prime factors for Mein likhe 2 into 2 into 2 into 2 into 2 into 2 into 7 into 7 theek hai yani ki the smallest number to be divided smallest number to be divided from 9408 such that the resulting number is a perfect square is 33136 Cup ka square root Kya Hoga yah Hoga iske liye ham har jo bhi hamare pass time factors keypad phone mein se ek hi tum living theek hai to usse Tu To le liya aur yahan se Saman le liya equal to 2 into 2 into 2 into 7 from 94083 such that the resulting number is a perfect square

and square root of the resulting number that is 3136 is 56

Example 7 - Chapter 6 Class 8 Squares and Square Roots

Last updated at Nov. 10, 2021 by

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Example 7 Find the smallest number by which 9408 must be divided so that the quotient is a perfect square. Find the square root of the quotient. Prime factorizing 9408 Prime factorizing 9408 We see that , 9408 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7 × 7 Since 3 does not occur in pairs, we divide by 3 to make it a pair So, our number becomes 9408 × 𝟏/𝟑 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7 × 7 × 𝟏/𝟑 3136 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 Square root of 3136 ∴ √3136 = 2 × 2 × 2 × 7 = 56 ∴ The smallest whole number to be divided = 3 and square root of new number = 56

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