By which smallest number 53240 be divided so that the quotient is a perfect cube number
|
Given : Show The given number is 53240. To do : We have to find the smallest number that should multiply 53240 to make it a perfect cube. Solution : To find the smallest number by which 53240 be multiplied to make it a perfect cube, we have to find the prime factors of it. Prime factorisation of 53240 is, $53240 = 2 \times 2 \times 2 \times 5 \times 11 \times 11 \times 11$ $= (2 \times 2 \times 2) \times 5 \times (11 \times 11 \times 11)$ $= 2^3 \times 5 \times 11^3$. As we can see, the given number is a product of 2 cube, 11 cube and 5. If we multiply the given number by 5 square it becomes a product of 2 cube, 5 cube and 11 cube. $53240 \times 5^2= 2^3 \times 5 \times 11^3\times 5^2$. $53240 \times 25 = 2^3 \times 5^3 \times 11^3$. $1331000 = (2\times 5\times 11)^3$. $1331000 = 110^3$. This implies, Cube root of 1331000 is 110. Therefore, the smallest number that has to be multiplied to make 53240 a perfect cube is 25 and the cube root of 1331000 is 110.
Register now for special offers  +91 Home > English > Class 8 > Maths > Chapter > Cubes And Cube Roots > Is 53240 a perfect cube? If no... UPLOAD PHOTO AND GET THE ANSWER NOW! Text Solution Solution : `53240 = 2xx2xx2xx5xx11xx11xx11 =2^3xx11^3xx5` Answer Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Add a public comment... Follow Us: Popular Chapters by Class: the given question says that is 532408 perfect cube if not then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube solve in this case in this question we are given two parts first first fall where they are supposed to check or find out whether 53240 is a perfect cube or not then we are supposed to find out is it is not a perfect cube then by which number should it be divided so as to get a perfect you so possible since we will we will use prime factorization method to check whether it is perfectly but not for that writing we are given the number is 532440 let's find out right it as a product of its prime factors so we have 532408 / to so we will get 26620 again it will get / to so we will get 13310 again it will get / to so we will get 6655 again it will not this time it's not getting / to because there is no even number at the units place now I will go y55l get 13319 1331 is only getting / 11 / 11 will get 121 no again 121 also can be divided by 11 so will get 11 11 11 by 1 CEO at the will get one know we can write 53240 is a product of these these prime factors so let's do that 53240 is equal to 2 x 2 x 2 x 5 x 11 X 11 X 11 sunao now I will check whether it is a perfect cube or not and to check if we will see whether the triplets are getting from the Knot hair 12 plate is getting home here another cricket is getting forms but 5 is not forming and triplet therefore 532440 is not a perfect cube so we can write the test 53240 is not a perfect perfect cube 240 not a perfect cube so the next vision was by what natural number should it be divided so that we can see that 5 is the only number which is not coming triplet so if we divide 532405 we will get a perfect cube show the answer to the second question is 53240 should be divided by 5 to form a perfect cube thank you Example 3 - Chapter 7 Class 8 Cubes and Cube RootsLast updated at Sept. 11, 2018 by
Support Teachoo in making more (and better content) - Monthly, 6 monthly, yearly packs available! TranscriptExample 3 Is 53240 a perfect cube? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube? We see that 53240 = 2 × 2 × 2 × 5 × 11 × 11 × 11 Here, 5 does not occur in triplets ∴ 53240 is not a perfect cube. So, we divide by 5 to make triplet So, our number becomes 53240 × 𝟏/𝟓 = 2 × 2 × 2 × 5 × 11 × 11 × 11 × 𝟏/𝟓 = 2 × 2 × 2 × 11 × 11 × 11 Now, it becomes a perfect cube. So, we divide 53240 by 5 to make it a perfect cube Is 53240 a perfect cube if not then?Solution : `53240 = 2xx2xx2xx5xx11xx11xx11 =2^3xx11^3xx5`
Thus, `53240` is not a perfect cube. What should be divided by 53240 to make it a perfect square?What should be divided by 53240 to make it a perfect cube? 53240/5 = 10648 is a perfect cube. 9.
How do you find the smallest number to be divided to get a perfect cube?Prime factorising 81, we get,. We know, a perfect cube has multiples of 3 as powers of prime factors.. Here, number of 3's is 4.. So we need to divide the factorization by 3 to make 81 a perfect cube.. Hence, the smallest number by which 81 must be divided to obtain a perfect cube is 3.. What is the smallest number by which 1600 so that the quotient is a perfect cube?Hence, 1600 is not a perfect cube. Hence, 25 is the required smallest number.
|
