Question

Find the smallest number by which 1100 much be multiplied so that the product becomes a perfect square . Also , find square root of the perfect square so obtained.​

Answer 1

$\underline{\underline {\quad{\textsf{\textbf{{Given\:: \quad}}}}} }$

• Find the smallest number by which 1100 much be multiplied so that the product becomes a perfect square . Also , find square root of the perfect square so obtained.

$\underline{\underline {\quad{\textsf{\textbf{{Solution\:: \quad}}}}} }$

$\\ \textsf{The prime factors of 1100 are} \\ \\ \\ \therefore \tt \: 2 \times 2 \times 5 \times 5 \times 11$

The number 11 is left unpaired. So, the given number must be multiplied by 11 to get the perfect square number.

$\\ \\ \therefore \tt \: 1100 \times 11 = 12100$

Now,

Square root of 12100 :

$\\ \\ \tt \: \sqrt{ 12100} = \sqrt{\underline{2 \times 2} \times\underline{ 5 \times 5} \times \underline{11 \times 11} } \\ \\ \\ \tt = 2 \times 5 \times 11 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: = { \underline{ \boxed{ \pmb{ \mathfrak{ \purple{110}}}}}} \: \: \bigstar\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence, square root of the new number is 110.