Question

What is the following quotient? Sqrt120/sqrt30

Answer 1

Answer: the required quotient is 2.

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

`Q=(√(120))/(√(30))~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

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

`(i)~√(x)=x^(1)/(2),\\\\(ii)~√(a* b)=\sqrt a* \sqrt b.`

From equation (i), we have

`Q\\\\\\=(√(120))/(√(30))\\\\\\=(√(4*30))/(√(30))\\\\\\=(\sqrt4*√(30))/(√(30))\\\\=√(2^2)\\\\=(2^2)^(1)/(2)\\\\=2^{2*(1)/(2)}\\\\=2.`

Thus, the required quotient is 2.

Answer 2

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

`(√(120))/(√(30))=\sqrt{(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