Question 21

A positive number exceed its positive square root by 30. Find the number.

Solution

According to the question,

$$(x-30)=√x$$ (where x is the positive number).

by taking square on both side,

$$(x-30)^2=(√x)^2$$

or,$$(x^2-60x+900)=x$$

or,$$(x^2-61x+900)=0$$

or,$$(x^2-25x-36x+900)=0$$

So,$$(x-25)(x-36)=0$$

or,$$x=25 and x=36$$

if $$x=25$$ then $$(25-30)=-5$$

but $$√25=5$$ which signifies that -5 is not equal to 5.

So,25 is not that number.

36 is the required number.

So,B is correct choice.

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