Question

When $ 15\sqrt {15} $ is divided by $ 3\sqrt 3 $, the quotient is

Answer 1

Hint: In this question, we are provided with two numbers. And we have to calculate the quotient on dividing one number with the other. Take the number with whom we are dividing the other number. Then choose the number with which product we can cancel the dividend term. And solving afterwards we can find the quotient.

Complete step by step solution:
In this question, we have to find the quotient on dividing the $ 3\sqrt 3 $ with $ 15\sqrt {15} $ .
Before dividing we need to know that the square root values will be subtracted from the square root vales and the outer numbers will be subtracted from the numbers itself. So, firstly multiplying the $ 3\sqrt 3 $ with $ 5 $ which will give the term $ 15 $ and the $ \sqrt {15} $ will be got on multiplying the $ \sqrt 3 $ with $ \sqrt 5 $ . Hence, we have to multiply the $ 3\sqrt 3 $ with $ 5\sqrt 5 $ to get the $ 15\sqrt {15} $
Hence, the quotient for the above question is $ 5\sqrt 5 $
This can also be solved by another method .
now the given question can be written as
 $ \Rightarrow \dfrac{{15\sqrt {15} }}{{3\sqrt 3 }} $
The number 15 is written as the product of 3 and 2, So now we have
 $ \Rightarrow \dfrac{{5 \times 3\sqrt {5 \times 3} }}{{3\sqrt 3 }} $
In the numerator and the denominator 3 is there and it will gets cancels and we have
 $ \Rightarrow \dfrac{{5\sqrt {5 \times 3} }}{{\sqrt 3 }} $
The square root is applicable to the both terms and it is written as
 $ \Rightarrow \dfrac{{5\sqrt 5 \times \sqrt 3 }}{{\sqrt 3 }} $
In the numerator and the denominator \[\sqrt 3 \] is there and it will gets cancels and it is written as
 $ \Rightarrow 5\sqrt 5 $
Hence, the quotient for the above question is $ 5\sqrt 5 $
So, the correct answer is “ $ 5\sqrt 5 $ ”.

Note: In this question, $ 15\sqrt {15} $ is the dividend $ 3\sqrt 3 $ is the divisor and dividing these we got $ 5\sqrt 5 $ as quotient and $ 0 $ is our remainder. We can also check our answer by using the dividend divisor remainder method. Where we can use the formula known as the remainder formula:
Dividend $ \div $ divisor $ = $ quotient $ + $ remainder $ \div $ divisor
Or can be written as
Dividend $ = $ Quotient $ \times $ divisor $ + $ remainder.
 $ 15\sqrt {15} $ $ = $ $ 5\sqrt 5 $ $ \times $ $ 3\sqrt 3 $ $ + $ $ 0 $
Which verified our answer.