Question

the smallest number by which 14700 should be divided so that it becomes a perfect square root the square root of the number obtained​

Answer 1

Answer:

3 is the smallest number by which 14700 divided to get a perfect square and square root is 70

Step-by-step explanation:

factorising 14700

14700=7*2100

=7*7*300

=7*7*3*10*10

to get a perfect square we need to divide it by 3

square root after dividing it will be 70

Answer 2

$\underline{\underline{\textsf{\textbf{\red{Given\::-}}}}}$

• Find the smallest number by which 14700 should be divided so that it becomes a perfect square - Also find the square root of the number obtained.

$\underline{\underline{\textsf{\textbf{\red{Solution\::-}}}}}$

$\begin{gathered} \textsf{The prime factors of 14700 are} \\ \\ \therefore \tt \: 2 \times 2 \times 3 \times 5 \times 5 \times 7 \times 7\end{gathered}$

• The number 3 is left unpaired. So, the given number must be divided NY and 3 to get the perfect square number.

$\begin{gathered} \\ \therefore \tt \: \frac{14700}{3} = 4900 \\ \end{gathered}$

Now,

$\begin{gathered} \tt \: \sqrt{ 4900} = \sqrt{\underline{2 \times 2} \times\underline{ 5 \times 5} \times \underline{7 \times 7} } \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt = 2 \times 5 \times 7 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: = 70\end{gathered}$

• Hence, square root of the new number is 70.