Question

Q4. Find the smallest number by which 2925 must be divided so that the quotient is a
perfect square. Find the square root of the quotient.​

Answer 1

Answer:

13 is perfect square. tyho

Answer 2

Solution :

$\bigstar$Firstly, we get L.C.M of 2925;

$\begin{array}{r|l} 3 & 2925 \\ \cline{2-2} 3 & 975 \\ \cline{2-2} 5 & 325 \\ \cline{2-2} 5 & 65 \\ \cline{2-2} 13 & 13 \\ \cline{2-2} & 1\end{array}$

Prime factorization of 2925 = 3 × 3 × 5 × 5 × 13

∴ 13 is not pair

The smallest number to be divided is 13

$\longrightarrow\sf{\cancel{\dfrac{2925}{13} }}\\\\\longrightarrow\bf{225}$

Square root :

$\longrightarrow\sf{\sqrt{225} =\sqrt{3\times 3\times 5\times 5} }\\\\\longrightarrow\sf{\sqrt{225} =\sqrt{(3)^{2} \times (5)^{2} } }\\\\\longrightarrow\sf{\sqrt{225}=3\times 5}\\\\\longrightarrow\bf{\sqrt{225} =15}$

Thus;

The number whose square is 225 is 15 .