Ex.6.3 Q8 Squares and Square Roots Solutions - NCERT Maths Class 8

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Question

\(2025\) 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 each row.

Text Solution

What is known?

Number of plants that is to be planted in the garden.

What is Unknown?

Number of rows and the number of plants in each row.

Reasoning:

Each row contains as many plants as the number of rows i.e. number of rows equal to number of plants in each row. Total number of plants that to be planted is equal to the product of number of plants and number of rows.

Steps:

Let number of rows be \(x\)

Number of plants in each row is also \(x\)

(number of rows) (number of plants in each row)  \(=2025\)

\[\begin{align}x \times x &= 2025\\{x^2} &= 2025\\x &= \sqrt {2025} \end{align}\]

\[\begin{align}&5\left| \!{\underline {\,{2025} \,}} \right. \\&5\left| \!{\underline {\,{405} \,}} \right. \\&3\left| \!{\underline {\,{81} \,}} \right. \\&3\left| \!{\underline {\,{27} \,}} \right. \\&3\left| \!{\underline {\,9 \,}} \right. \\&3\left| \!{\underline {\,3 \,}} \right. \\&1\left| \!{\underline {\,1 \,}} \right. \end{align}\]

\[\begin{align}x &= \sqrt {2025} \\x &= \sqrt {5 \times 5 \times 3 \times 3 \times 3 \times 3} \\x &= \sqrt {{5^2} \times {3^2} \times {3^2}} \\x &= \sqrt {{{(5 \times 3 \times 3)}^2}} \\x &= 5 \times 3 \times 3 = 45\end{align}\]

Therefore, the number of rows and the number of plants in each row is \(45\).