Question

Find the least number to be added to 1467 so as to get a perfect square. Also, find the square root of the perfect square number so obtained​

Answer 1

Answer:

54

Step-by-step explanation:

In square roots, two numbers in factorisation should be equally cancelled to get the number itself:

Ex: $\sqrt{4} = \sqrt{2 * 2} = 2$

Two numbers inside the square (√)root would get it outside with power 1

Three numbers inside the cube root(∛) would get it outside with power 1

So, perfect square means the number will not leave any remains in the root

Now,

To the real question

Factorising the number, we will get

$\sqrt{1467} = \sqrt{3 * 3 * 163}$

So taking the numbers outside we will get

$\sqrt{1467} = 3 \sqrt{163}$

Add 1467 with 54 which gives you 1521

Factorising 1521 , we will get

$\sqrt{1521} = \sqrt{3 * 3 * 13 * 13}$

$\sqrt{1521} = \sqrt{3^{2} * 13^{2} }$

$\sqrt{1521} = 3 * 13$

$\sqrt{1521} = 39$

So, when 1467 added with 54 gives us a perfect square.

Thus, 54 is the answer

Answer 2

Answer:

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