Question

How do you simplify 5 over square root of 7?

Answer 1

Hint: In this problem, we have to simplify 5 over square root of 7. We can first convert the given statement into a mathematical form to simplify it. We will get a mathematical form as \[\dfrac{5}{\sqrt{7}}\]. We have to analyse the fraction as the numerator 5 and the denominator 7, both are prime numbers, so we cannot simplify to its simplest form, but we can simplify by taking the denominator to the numerator or we can multiply both numerator and the denominator by \[\sqrt{7}\].

Complete step by step solution:
We know that the statement given to be simplified is,
‘5 over square root of 7’.
We can convert the given statement into a mathematical form to simplify it.
\[\dfrac{5}{\sqrt{7}}\]
We can now convert the square root in the denominator to the fractional power, we get
\[\Rightarrow \dfrac{5}{{{7}^{\dfrac{1}{2}}}}\]
Now we can take the denominator to the numerator, by changing the sign of the power, we get
\[\Rightarrow 5\times {{7}^{-\dfrac{1}{2}}}\]

Therefore, the simplified form of the given statement is \[\dfrac{5\sqrt{7}}{7}\].

Note: We can also simplify the given problem in another method.
We know that the statement given to be simplified is,
‘5 over square root of 7’.
We can convert the given statement into a mathematical form to simplify it.
\[\dfrac{5}{\sqrt{7}}\]
We can multiply both numerator and the denominator by \[\sqrt{7}\], we get
\[\Rightarrow \dfrac{5}{\sqrt{7}}\times \dfrac{\sqrt{7}}{\sqrt{7}}\]
Now we can multiply the above step, we get
\[\Rightarrow \dfrac{5\sqrt{7}}{7}\]
\[\because \sqrt{7}\times \sqrt{7}=7\]