Question 52

By what least number 25 x 20 x 9 x 12 x 30 should be multiplied to make it a perfect square number ?

Solution

Expression : 25 x 20 x 9 x 12 x 30

= $$(5^2)\times(2^2\times5)\times(3^2)\times(2^2\times3)\times(2\times3\times5)$$

= $$(2^5)\times(3^4)\times(5^4)$$

To make above number a perfect square, all the exponents must be even, thus the smallest number which should be multiplied = $$2$$

=> Ans - (D)

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