Question

 The value of $\sqrt {900} + \sqrt {0.09} - \sqrt {0.000009} $is
A.30.297
B.30.197
C.30.097
D.30.397

Answer 1

Hint: To solve the square roots of the given equation, we will try to simplify their values and then we will obtain the answer. For example, 0.09 can be written as $\dfrac{9}{{100}}$which is quite easier to take the under-root value of the number.

Step by step solution:

Here, we will first simplify the terms of the given equation: $\sqrt {900} + \sqrt {0.09} - \sqrt {0.000009} $
Firstly considering $\sqrt {900} $ , this is clearly visible and already known that $\sqrt {900} = 30$.
Considering the second term of the equation$\sqrt {0.09} $,
we can write 0.09 as $\dfrac{9}{{100}}$. Taking square roots of both numerator and the denominator, we get
$\sqrt {0.09} = \sqrt {\dfrac{9}{{100}}} = \sqrt {\dfrac{{3 \times 3}}{{10 \times 10}}} = \dfrac{3}{{10}}$
$ \Rightarrow \sqrt {0.09} = 0.3$
Simplifying the third term of the given equation $\sqrt {0.000009} $, we get
$\sqrt {0.000009} = \sqrt {\dfrac{9}{{1000000}}} = \sqrt {\dfrac{{3 \times 3}}{{1000 \times 1000}}} = \dfrac{3}{{1000}}$
$ \Rightarrow \sqrt {0.000009} = 0.003$
Therefore, substituting the values of$\sqrt {900} $, $\sqrt {0.09} $and $\sqrt {0.000009} $in the given equation $\sqrt {900} + \sqrt {0.09} - \sqrt {0.000009} $, we get
$
   \Rightarrow \sqrt {900} + \sqrt {0.09} - \sqrt {0.000009} = 30 + 0.3 - 0.003 \\
   \Rightarrow \sqrt {900} + \sqrt {0.09} - \sqrt {0.000009} = 30.297 \\
 $
Hence, the value of $\sqrt {900} + \sqrt {0.09} - \sqrt {0.000009} $ is found to be 30.297.
Therefore, option(A) is correct.

Note: In such problems, students generally use a calculator or long division method to determine the values of the square root of the number. It is a more time consuming and lengthy process to carry forward. You can just simplify them or break the digit whose square root is asked. Simplifying them into a much simpler form can be helpful and can be done in considerably less time.