14. Find the smallest number by which 2925 must be difind the square r

1.	14. Find the smallest number by which 2925 must be difind the square root of the perfect square so obtained.15. 1225 plants are to be planted in a garden in such a way that each row contains asmany plants as the number of rows. Find the number of rows and the number of plants in
Answer» 1. First, we NEED to do prime factorization of 2925. $\begin{array}{r \| l} 3 & 2925 \\ \cline{<klux>2</klux>-2} 3 & 975 \\ \cline{2-2} 5 & 325 \\ \cline{2-2} 5 & 65 \\ \cline{2-2} & 13 \\ \end{array}$ 2925 ⇒ $(3\times 3)\times (5\times 5)\times 13$ ∴ 13 doesn't have a PAIR. So 13 is the smallest number that can be divided by 2925 to get a perfect square. $2925\div 13=225$ Now lets prime factorize 225 to get the square root. $\begin{array}{r \| l} 3 & 225 \\ \cline{2-2} 3 & 75 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} & 5 \\ \end{array}$ 225 ⇒ $(3\times 3)\times (5\times5)$ Now we need to TAKE one number from each pair to find the square root. $\sqrt{225}=3\times5$ $\sqrt{225}=15$ ∴So the square root of the perfect square is ⇒ $\sqrt{225}=15$ 2. Number of plants ⇒ 1225 Number of plants in each row ⇒ $\sqrt{1225}$ To find $\sqrt{1225}$ we need to prime factorize it. $\begin{array}{r \| l} 5 & 1225 \\ \cline{2-2} 5 & 245 \\ \cline{2-2} 7 & 49 \\ \cline{2-2} & 7 \\ \end{array}$ 1225 ⇒ $(5\times 5)\times (7\times 7)$ Now we need to take one number from each pair to find the square root. $\sqrt{1225}=5\times 7$ $\sqrt{1225}=35$ ∴ 35 plants will be in each row.

14. Find the smallest number by which 2925 must be difind the square root of the perfect square so obtained.15. 1225 plants are to be planted in a garden in such a way that each row contains asmany plants as the number of rows. Find the number of rows and the number of plants in

Answer»

1. First, we NEED to do prime factorization of 2925.

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

2925 ⇒ $(3\times 3)\times (5\times 5)\times 13$

∴ 13 doesn't have a PAIR. So 13 is the smallest number that can be divided by 2925 to get a perfect square.

$2925\div 13=225$

Now lets prime factorize 225 to get the square root.

$\begin{array}{r | l} 3 & 225 \\ \cline{2-2} 3 & 75 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} & 5 \\ \end{array}$

225 ⇒ $(3\times 3)\times (5\times5)$

Now we need to TAKE one number from each pair to find the square root.

$\sqrt{225}=3\times5$

$\sqrt{225}=15$

∴So the square root of the perfect square is ⇒ $\sqrt{225}=15$

2. Number of plants ⇒ 1225

Number of plants in each row ⇒ $\sqrt{1225}$

To find $\sqrt{1225}$ we need to prime factorize it.

$\begin{array}{r | l} 5 & 1225 \\ \cline{2-2} 5 & 245 \\ \cline{2-2} 7 & 49 \\ \cline{2-2} & 7 \\ \end{array}$

1225 ⇒ $(5\times 5)\times (7\times 7)$

Now we need to take one number from each pair to find the square root.

$\sqrt{1225}=5\times 7$

$\sqrt{1225}=35$

∴ 35 plants will be in each row.