Question

How do you simplify (square root of 6/square root of 7)*(square root of 14/square root of 3)?

Answer 1

Hint: To solve the given question, we should know the algebraic properties. The first property we should know is that the square root of a number can be expressed algebraically as \[\sqrt{a}\]. We will use different properties of this square root. We can also express \[\dfrac{\sqrt{a}}{\sqrt{b}}\] as \[\sqrt{\dfrac{a}{b}}\]. Also, we should first express the given word statement in an algebraic equation. We should also know the rule which states that, by multiplying two similar quantities, square of it.

Complete step by step solution:
We are given the (square root of 6/square root of 7)*(square root of 14/square root of 3). As we know that the square root of a number can be expressed algebraically as \[\sqrt{a}\]. Using this, we can express the statement as \[\dfrac{\sqrt{6}}{\sqrt{7}}\times \dfrac{\sqrt{14}}{\sqrt{3}}\]
Rearranging the terms of the above equation to simplify it, we get
\[\dfrac{\sqrt{6}}{\sqrt{3}}\times \dfrac{\sqrt{14}}{\sqrt{7}}\]
Using the property of square roots which states that, we can also express \[\dfrac{\sqrt{a}}{\sqrt{b}}\] as \[\sqrt{\dfrac{a}{b}}\]
\[\Rightarrow \sqrt{\dfrac{6}{3}}\sqrt{\dfrac{14}{7}}\]
Simplifying the above equation, we get the values as
\[\Rightarrow \sqrt{2}\sqrt{2}\]
Multiplying two similar quantities gets square of it. Using this principle, we get the values as
\[\Rightarrow {{\left( \sqrt{2} \right)}^{2}}\]
Using the property which states that \[{{\left( \sqrt{a} \right)}^{2}}=a\] , the above expression gives values as
\[\Rightarrow 2\]
Thus, the value of the given expression is 2.

Note: one can do calculation mistakes while solving these questions, so it should be avoided. The properties of square root function should be remembered, as well as square and square root of numbers.