Question

If we have a square root as \[\sqrt{1.21}=1.1\], then \[\sqrt{.000121}\] is equal to
(A). 0.0011
(B). 0.011
(C). 0.11
(D). 11.0

Answer 1

Hint: Multiply and divide with 10 inside the square root. Just simplify the numerator and denominator separately. Repeat this process until you get the value of the number for which you already know the square root. Now substitute that value here and convert the square root into powers of \[\dfrac{1}{2}\] in the denominator. And then again continue to shift the decimal point to reach the decimal value result you require.

Complete step-by-step solution -
Decimals: - The decimal numerical system is the standard system for denoting integer and non – integer numbers. It is an extension to non – integer numbers of the Hindu – Arabic numerical system. This way of notation is called decimal notation. We say the decimal part and the whole number part is separated by a decimal point. The digits after that point show a value smaller than one.
Given square root of a number in the question is:
\[\Rightarrow \] \[\sqrt{1.21}=1.1\].
The number for which we need to find square root is:
\[\Rightarrow \] 0.000121.
We need to convert this number into the form of 1.21.
By multiplying and dividing with 10, to the number, we get:
\[\Rightarrow \dfrac{0.000121}{10}\times 10=\dfrac{0.00121}{10}\]
By multiplying and dividing with 10 to above number, we get:
\[\Rightarrow \dfrac{0.00121\times 10}{10\times 10}=\dfrac{0.0121}{{{10}^{2}}}\]
By multiplying and dividing with 10 again, we get it as:
\[\Rightarrow \dfrac{1.21}{{{10}^{4}}}=0.000121\]
By applying square root on both sides, we get it as:
\[\Rightarrow \sqrt{0.000121}=\sqrt{\dfrac{1.21}{{{10}^{4}}}}\]
By basic knowledge of algebra, we say \[\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}\].
Now simplifying above equation and lowerting root to power:
\[\Rightarrow \sqrt{0.000121}=\dfrac{\sqrt{1.21}}{{{\left( {{10}^{4}} \right)}^{\dfrac{1}{2}}}}=\dfrac{\sqrt{1.21}}{{{10}^{2}}}\]
By substituting the value and simplifying, we get it as:
\[\Rightarrow \sqrt{0.000121}=\dfrac{1.1}{100}=0.011\]
Therefore, option (b) is the correct answer for a given question.

Note: You can directly multiply and divide by \[{{10}^{4}}\] but here it is solved step by step to make you understand the reason. Be careful while applying square root properties as it is the main point in the question. After getting the result multiply it with itself and just verify that you are getting the given number or not.