Question

How do you find the square root of 14 divided by the square root of 77?

Answer 1

Hint: In the given question, we have been asked to find the value of the square root of 14 divided by the square root of 77. In order to find the value, first we need to apply the law of radical which states that \[\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b}}\]. Later we will need to simplify the numbers by converting them into the simplest form. Then we will need to rationalize the denominator and we will get our required answer.

Complete step by step solution:
We have given that,
Square root of 14 is divided by square root of 77, i.e.
\[\Rightarrow \dfrac{\sqrt{14}}{\sqrt{77}}\]
Using the radical laws which states that \[\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b}}\].
By applying this property in the given radical, we obtain
\[\Rightarrow \dfrac{\sqrt{14}}{\sqrt{77}}=\sqrt{\dfrac{14}{77}}\]
Converting the fraction in the square root into simplest form, we get
Dividing both the numbers by 7, we get
\[\Rightarrow \sqrt{\dfrac{14}{77}}=\sqrt{\dfrac{2}{11}}\]
\[\Rightarrow \sqrt{\dfrac{2}{11}}\]
Multiply and divide the above fraction by \[\sqrt{11}\], we get
\[\Rightarrow \sqrt{\dfrac{2}{11}}\times \dfrac{\sqrt{11}}{\sqrt{11}}\]
Simplifying the above we will get,
\[\Rightarrow \dfrac{2\sqrt{11}}{11}\]

Thus,
\[\Rightarrow \dfrac{\sqrt{14}}{\sqrt{77}}=\dfrac{2\sqrt{11}}{11}\]
Hence, this is the required answer.

Note: Students need to remember the laws of radicals while solving the question. They have to keep in mind that if there is root in the denominator then they rationalize the given radical, that is they need to multiply the numerator and the denominator by the same value of the denominator to remove the root from the denominator. Students need to check the digits while putting them down and doing calculations to avoid making any types of errors.