Question

Find the smallest by which 1100 must be multiplied so that the product been square, also find the square root of the perfect square so obtained

Answer 1

Answer:

The prime factorization of 1100

2. 1100

2. 550

5. 275

5. 55

11 11

1

Since 11 is not in pairs we'll multiply 1100 with 11

1100×11

12100

The prime factorization of 12100

2 12100

2 6050

5 3025

5 605

11 121

11 11

1

2×5×11

110

Answer 2

Answer:

The smallest number by which 1100 must be multiplied so a square number is formed is 11. The square root of the perfect square is 110.

Step-by-step explanation:

The number = 1100

The smallest number which will be multiplied to 1100 so that a perfect square is obtained = ??

Prime Factorize 1100,

$\begin{array}{r|l} 2 & 1100\\\cline{1-2} 2 & 550 \\\cline{1-2} 5 & 275 \\ \cline{1-2} 5 & 55\\\cline{1-2} 11& 11 \\\cline{1-2} & 1 \end{array}$

1100 = 2 × 2 × 5 × 5 × 11  

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Only, 11 doesn't have any pair, which means, 1100 should be multiplied by 11.

Multiply by 11 -

⇒ 1100 × 11

⇒ 12100

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Square root of 12100,

$\begin{array}{r|l} 2 & 12100\\\cline{1-2} 2 & 6050 \\\cline{1-2} 5 & 3025 \\ \cline{1-2} 5 & 605\\\cline{1-2} 11 & 121 \\\cline{1-2} 11 & 11 \\\cline{1-2} &1 \end{array}$

⇒ 12100 = 2 × 2 × 5 × 5 × 11 × 11

⇒ √12100 = 2 × 5 × 11

⇒ √12100 = 110

Square root of 12100 is 110.

∴ The smallest number by which 1100 must be multiplied so a square number is formed is 11. The square root of the perfect square is 110.