Question

14. Find the smallest number by which 2925 must be di
find 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 as
many plants as the number of rows. Find the number of rows and the number of plants in​

Answer 1

Answer:

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Answer 2

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

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

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.