Question

the smallest natural number by which 1200should be multiplied so that the square root of the product is rational number.

1. 3
2. 2
3. 1
4. 4 ​

Answer 1

Answer:

Hence, 1200 must be multiplied by 3 so that the square root of the product is a rational number.

Answer 2

Answer:

We have 1200,

We first factorise the number "1200":

1200=2\times 2\times 2\times 2\times \times 3\times 5\times 51200=2×2×2×2××3×5×5

We can see that 3 has no pair.

To make it a perfect square, we will multiply by 3 on both the sides.

\begin{gathered}1200\times 3=2\times 2\times 2\times 2\times 3\times 3\times 5\times 5\\\\\sqrt{3600}=\sqrt{2\times 2\times 2\times 2\times 3\times 3\times 5\times 5}\\\\\sqrt{3600}=2\times 2\times 3\times 5\\\\\sqrt{3600}=60\end{gathered}

1200×3=2×2×2×2×3×3×5×5

3600

=

2×2×2×2×3×3×5×5

3600

=2×2×3×5

3600

=60

HOPE IT IS HELP YOU