Question

What is the following quotient? Sqrt120/sqrt30

Answer 1

Since both numbers are under the square root sign they can be combined under 1 sqrt sign.

$\dfrac{\sqrt{120}}{\sqrt{30}}=\sqrt{\dfrac{120}{30}}$

Now all you need do is perform the division under the root sign

sqrt(4) is your answer but not the final one.

2 <<<<< Answer

Answer 2

Answer:  the required quotient is 2.

Step-by-step explanation:  We are given to find the following quotient :

$Q=\dfrac{\sqrt{120}}{\sqrt{30}}~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following properties of radicals and exponents :

$(i)~\sqrt{x}=x^\frac{1}{2},\\\\(ii)~\sqrt{a\times b}=\sqrt a\times \sqrt b.$

From equation (i), we have

$Q\\\\\\=\dfrac{\sqrt{120}}{\sqrt{30}}\\\\\\=\dfrac{\sqrt{4\times30}}{\sqrt{30}}\\\\\\=\dfrac{\sqrt4\times\sqrt{30}}{\sqrt{30}}\\\\=\sqrt{2^2}\\\\=(2^2)^\frac{1}{2}\\\\=2^{2\times\frac{1}{2}}\\\\=2.$

Thus, the required quotient is 2.