QUESTION

Find the value of:(a). $\dfrac{\sqrt{100\text{x225}}}{\sqrt{289-33}}$(b). $\dfrac{\sqrt{225}+\sqrt{49}}{\sqrt{64}-\sqrt{36}}$

Hint: To proceed this question, we need to know the basic BODMAS rule of mathematics for solving mathematical equations. In this rule we need to solve the brackets which are given by B, O which stands for “of”, D for division M for multiplication and A for addition and lastly S for subtraction.

Complete step-by-step solution -

(a) Also, we need to understand the meaning of square root. A square root is a number which produces a specified quantity when multiplied by itself. For example, 7 is a square root of 49.
So, in the first question we are given to solve $\dfrac{\sqrt{100\text{x225}}}{\sqrt{289-33}}$.
To proceed this, we will first of all solve the numerator inside of the square root and then go for taking the square root of the given expression to get the answer.
We have,
$\dfrac{\sqrt{100\text{x225}}}{\sqrt{289-33}}=\dfrac{\sqrt{\text{22500}}}{\sqrt{256}}$
Taking the square root on the right-hand side of both the numerator and the denominator,
$\Rightarrow \dfrac{\sqrt{100\text{x225}}}{\sqrt{289-33}}=\dfrac{150}{16}$
Solving the expression obtained on the right-hand side of the above obtained expression,
$\Rightarrow \dfrac{\sqrt{100\text{x225}}}{\sqrt{289-33}}=9.375$
Hence, we got the answer of the part (a) of the question as,
$\dfrac{\sqrt{100\text{x225}}}{\sqrt{289-33}}=9.375$.

(b)$\dfrac{\sqrt{225}+\sqrt{49}}{\sqrt{64}-\sqrt{36}}$
Now we will proceed to solve the second question similarly as done above.
In this we first of all have to solve the square root of both the denominator and numerator and then go for adding or subtracting, because the addition sign and the subtraction sign does not come under the square root.
Doing so we get,
$\dfrac{\sqrt{225}+\sqrt{49}}{\sqrt{64}-\sqrt{36}}=\dfrac{15+7}{8-6}$
Doing necessary calculations on the right-hand side of the above obtained expression we get,
\begin{align} & \Rightarrow \dfrac{\sqrt{225}+\sqrt{49}}{\sqrt{64}-\sqrt{36}}=\dfrac{22}{2} \\ & \Rightarrow \dfrac{\sqrt{225}+\sqrt{49}}{\sqrt{64}-\sqrt{36}}=11 \\ \end{align}
Therefore, we got the answer of part (b) as,
$\dfrac{\sqrt{225}+\sqrt{49}}{\sqrt{64}-\sqrt{36}}=11$

Note: The possibility of error in this type of question is not following Bodmas rule and just going for normal calculation should give incorrect results, because taking the square root and then adding gives different answers then adding the term first and then taking the square root of it.