Is 9408 a perfect square if not find the smallest number by which 9408 must be a multiplied?

Chapter 3 Squares and Square Roots – Exercise 3.1 | Set 1

Question 9. Find the greatest number of two digits which is a perfect square.

Solution:

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• Chapter 3 Squares and Square Roots – Exercise 3.1 | Set 1
• Question 9. Find the greatest number of two digits which is a perfect square.
• Question 10. Find the least number of three digits which is a perfect square.
• Question 11. Find the smallest number by which 4851 must be multiplied so that the product becomes a perfect square.
• Question 12. Find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square.
• Question 13. Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also find the number whose square is the resulting number.
• 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 Read more on Brainly.in - https://brainly.in/question/15823#readmore (adsbygoogle = window.adsbygoogle || []).push({});
• Example 7 - Chapter 6 Class 8 Squares and Square Roots
• What number must be multiplied to 9408 to make it perfect square?
• What is the least number by which 9408 divided that the quotient is a perfect square?
• What is the perfect square of 4931?
• What is the smallest multiple of 2352 which is a perfect square?

Greatest two-digit number is 99

99 = 81+18

= 9×9 + 18

18 is the remainder

 Perfect square number is 99 – 18 = 81

Therefore, the greatest number of two digits which is perfect square is 81

Question 10. Find the least number of three digits which is a perfect square.

Solution:

Least three-digit number is 100

100 = 10 × 10

100 itself is the square of 10

Therefore, the least number of three digits which is perfect square is 100

Question 11. Find the smallest number by which 4851 must be multiplied so that the product becomes a perfect square.

Solution:

Prime factorization of 4851

4851 = 3×3×7×7×11

By grouping the prime factors 

= (3×3) × (7×7) × 11

11 is left out

Therefore, the smallest number by which 4851 must be multiplied so that the product becomes a perfect square is 11.

Question 12. Find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square.

Solution:

Prime factorization of 28812

28812 = 2×2×3×7×7×7×7

By grouping the prime factors

= (2×2) × 3 × (7×7) × (7×7)

3 is left out

Therefore, the smallest number by which 28812 must be divided so that the quotient becomes a perfect square is 3.

Question 13. Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also find the number whose square is the resulting number.

Solution:

Prime factorization of 1152

1152 = 2×2×2×2×2×2×2×3×3

By grouping the prime factors

= (2×2) × (2×2) × (2×2) × (3×3) × 2

Therefore, the smallest number by which 1152 must be divided so that the quotient becomes a perfect square is 2.

The number after division, 1152/2 = 576

Prime factors for 576 = 2×2×2×2×2×2×3×3

By grouping the prime factors

= (2×2) × (2×2) × (2×2) × (3×3)

= (2×2×2×3) × (2×2×2×3)

= 242

Therefore, the resulting number is square of 24.

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 Read more on Brainly.in - https://brainly.in/question/15823#readmore (adsbygoogle = window.adsbygoogle || []).push({});

Example 7 - Chapter 6 Class 8 Squares and Square Roots

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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

What number must be multiplied to 9408 to make it perfect square?

9408/3+ 3136 = 2*2*2*2*2*2*7*7. Which is perfect square.

What is the least number by which 9408 divided that the quotient is a perfect square?

So, 3 is the number by which 9408 must be divided to make the quotient a perfect square.

What is the perfect square of 4931?

so 110 must be added to 4931 to get a perfect Square. Was this answer helpful?

What is the smallest multiple of 2352 which is a perfect square?

So, we will multiply the number 2352 with 3 to make it a perfect square. Now, to verify that 3 is the smallest number which is multiplied to 2352 to make it a perfect square, we need to multiply 3 with the number and then find its square root. Hence, the number is a perfect square and the perfect square is 84.

Is 9408 a perfect square if not find the smallest number by which 9408 must be a multiplied b divided so as to make it a perfect square?

Is 9408 a perfect square if not find the smallest multiple of 9408 which is a perfect square find the square root of new number?

Is 9408 a perfect square find the smallest number?

What number must be multiplied to 9408 to make it perfect square?