What is the smallest number by which 3087 may be multiplied so that the product is a perfect cube?
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No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Which of the following is perfect cube? 106480 On factorising 106480 into prime factors, we get: \[106480 = 2 \times 2 \times 2 \times 2 \times 5 \times 11 \times 11 \times 11\] Group the factors in triples of equal factors as: \[106480 = \left\{ 2 \times 2 \times 2 \right\} \times 2 \times 5 \times \left\{ 11 \times 11 \times 11 \right\}\] It is evident that the prime factors of 106480 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 106480 is a not perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Page 2Which of the following is perfect cube? 166375 On factorising 166375 into prime factors, we get: \[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\] Group the factors in triples of equal factors as: \[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\] It is evident that the prime factors of 166375 can be grouped into triples of equal factors and no factor is left over. Therefore, 166375 is a perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Page 3Which of the following is perfect cube? 456533 On factorising 456533 into prime factors, we get: \[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\] Group the factors in triples of equal factors as: \[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\] It is evident that the prime factors of 456533 can be grouped into triples of equal factors and no factor is left over. Therefore, 456533 is a perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Factorise: x4 - 1 Solution: Explanation: We know that, a2-b2=(a+b)(a-b) So we will have, x4-1=x4-14 x4-1=(x2)2-(12)2 x4-1=(x2+12)(x2-12) x4-1=(x2+1)(x+1)(x-1) Final Answer: x4-1=(x2+1)(x+1)(x-1) Find the diagonal of a square whose side is 12 cm Solution: Explanation: The length diagonal of a square of side a=2a Substituting a=12cm, we get, Length of the diagonal =212 cm =122 cm Taking 2=1.414 We will get the length as, 12(1.414) = 16.93 cm Final Answer: The diagonal of a square whose side is 12 cm is 16.93 cm. In a certain store the profit is 320% of the cost If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? A: 30% B: 100% C: 70% D: 250% Solution: Explanation: Using the formula to solve the given problem:- Profit = selling price - cost price; % of profit in selling price = prof price / selling price×100 Let the cost price be x then profit = 320 % × x=3.2x Selling price = Cost price + profit = x+3.2x =4.2x After increasing C.P. by 25% = 125%× x=1.25x Profit = selling price - cost price =4.2x-1.25x =2.95x % of profit in selling price = prof price / selling price×100 2.95 / 4.25 ×100 =70% Final answer: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately 70% of the selling price is the profit. What is the ordinate of any point on x axis Solution: Explanation: According to the question,to find the ordinate of a point lying on the x-axis. The ordinate of a point lying in space is the y-coordinate. Any point lying on the two-dimensional plane will have some value of x-coordinate and some value of y -coordinate Ordinate is y coordinate. On the x-axis, the y coordinate is 0. Final answer: Ordinate of any point on the x-axis is 0. Number which is divisible by 2 is A: 7,907 B: 63,195 C: 72,028 D: 3,451 Solution: Explanation: The all even numbers are divisible by 2. The divisibility of 2 :- A number which is always ends with 0,2,4,6,8. The digit is ends with number 8 which is divisible by 2. Final answer: 72028 is divisible by 2. Hence, the correct option is C i.e. 72028. Which of the following is perfect cube? 106480 On factorising 106480 into prime factors, we get: \[106480 = 2 \times 2 \times 2 \times 2 \times 5 \times 11 \times 11 \times 11\] Group the factors in triples of equal factors as: \[106480 = \left\{ 2 \times 2 \times 2 \right\} \times 2 \times 5 \times \left\{ 11 \times 11 \times 11 \right\}\] It is evident that the prime factors of 106480 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 106480 is a not perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Page 2Which of the following is perfect cube? 166375 On factorising 166375 into prime factors, we get: \[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\] Group the factors in triples of equal factors as: \[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\] It is evident that the prime factors of 166375 can be grouped into triples of equal factors and no factor is left over. Therefore, 166375 is a perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Page 3Which of the following is perfect cube? 456533 On factorising 456533 into prime factors, we get: \[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\] Group the factors in triples of equal factors as: \[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\] It is evident that the prime factors of 456533 can be grouped into triples of equal factors and no factor is left over. Therefore, 456533 is a perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Which of the following is perfect cube? 106480 On factorising 106480 into prime factors, we get: \[106480 = 2 \times 2 \times 2 \times 2 \times 5 \times 11 \times 11 \times 11\] Group the factors in triples of equal factors as: \[106480 = \left\{ 2 \times 2 \times 2 \right\} \times 2 \times 5 \times \left\{ 11 \times 11 \times 11 \right\}\] It is evident that the prime factors of 106480 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 106480 is a not perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Page 2Which of the following is perfect cube? 166375 On factorising 166375 into prime factors, we get: \[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\] Group the factors in triples of equal factors as: \[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\] It is evident that the prime factors of 166375 can be grouped into triples of equal factors and no factor is left over. Therefore, 166375 is a perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? Page 3Which of the following is perfect cube? 456533 On factorising 456533 into prime factors, we get: \[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\] Group the factors in triples of equal factors as: \[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\] It is evident that the prime factors of 456533 can be grouped into triples of equal factors and no factor is left over. Therefore, 456533 is a perfect cube. Concept: Concept of Cube Root Is there an error in this question or solution? What is the smallest number with which 4860 must be multiplied to make it a perfect cube?Hence, the smallest number by which 4860 should be multiplied so that the product is a perfect cube is 150. What is the smallest number by which 2592 must be multiplied so that the product is a perfect cube?∴ The given number should be multiplied by 3187. What is the smallest number by which 10584 may be multiplied so that the product is a perfect cube also find the cube root of the number obtained?Hence, the smallest number by which 10584 must be multiplied to obtain a perfect cube is 7. What is the smallest number by which 3087 may be multiplied so that the product is a?Hence, the smallest number by which 3087 must be multiplied to obtain a perfect cube is 3. What is the perfect cube of 3087?Step-by-step explanation:
Since the number 3 has not triplet, Therefore we need to multiply 3087 by 3 to make it a perfect cube.
What is the smallest number by which 3087 must be divided so that the quotient is a perfect cube *?And, it can be removed by dividing it by that number. And, we obtain a perfect cube, as $7 \times 7 \times 7 = 343$ and $\sqrt[3]{{343}} = 7$. Therefore, the smallest number which can be divided from $3087$ to get the quotient as a perfect cube is $3 \times 3 = 9$.
What is the smallest number by which 4116 must be multiplied to obtain a perfect cube?∴ We must multiply 18 (2×3×3) to make 4116 a perfect cube.
What is the smallest number by which 106480 may be multiplied so that the product is a perfect cube?This is Expert Verified Answer
So the smallest number by which 106480 can be multiplied to become a perfect cube is 100.
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