Question

If the square root of $5625$ is $75$ then $\sqrt {5625} + \sqrt {56.25} + \sqrt {0.5625} $ is equal to
$\left( a \right){\text{ 9}}$
$\left( b \right){\text{ 83}}{\text{.25}}$
$\left( c \right){\text{ 82}}{\text{.80}}$
$\left( d \right){\text{ 8}}{\text{.325}}$

Answer 1

Hint: This type of question becomes tricky and if the values of a similar number are already given. So in this question, we will first just remove the decimal and then the square root of the numerator and denominator can be solved easily. And in this way, we will solve this question.

Complete step-by-step answer:
So in the question, it is given that the $\sqrt {5625} = 75$ . And we have to find it $\sqrt {5625} + \sqrt {56.25} + \sqrt {0.5625} $ . So for this, we will remove the decimal and then will solve it accordingly.
So, $\sqrt {56.25} = \sqrt {\dfrac{{5625}}{{100}}} $ and the above square root can also be written as
$ \Rightarrow \dfrac{{\sqrt {5625} }}{{\sqrt {100} }}$
And by using the values given to us and we know the square root of $100$ is $10$ and also dividing the number and therefore, we get
$ \Rightarrow \sqrt {56.25} = \dfrac{{75}}{{10}} = 7.5$
Similarly,
$ \Rightarrow \sqrt {0.5625} = \sqrt {\dfrac{{5625}}{{10000}}} $ and the above square root can also be written as
$ \Rightarrow \dfrac{{\sqrt {5625} }}{{\sqrt {10000} }}$
And by using the values given to us and we know the square root of $100$ is $10$ and also on dividing the number and therefore, we get
$ \Rightarrow \sqrt {0.5625} = \dfrac{{75}}{{100}} = 0.75$
So we have all the values of the square root. Now we will add these square roots.
$ \Rightarrow \sqrt {5625} + \sqrt {56.25} + \sqrt {0.5625} $
On substituting the values we had obtained above, we get
$ \Rightarrow 75 + 7.5 + 0.75$
Therefore, on adding all these, we get
$ \Rightarrow 83.25$
So, $\sqrt {5625} + \sqrt {56.25} + \sqrt {0.5625} $ will be equal to $83.25$ .
Hence, the option $\left( b \right)$ is correct.

Note: For solving this type of question we should always try to divide the number into the perfect squares because it makes the calculation easier. And then we should take the square root of our perfect square factors. After this, we can reduce the answer to the simplest forms. If our number doesn’t factor in or match perfectly.