Question

Multiply 1681000 by the smallest number so that the product is a perfect cube. Also, find out the cube root of the product.

with solution
step-by-step​

Answer 1

Solution:-

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Here, the question had given a digit and had asked to multiply 1681000 by the smallest number so that product is a perfect cube. So first of all we need to do prime factorisation for 1681000. Then after we will make out pairs and after that we have to multiply the numbers which are not making pair of 3 to make the number a perfect cube. Product that we will get after multiplying the the numbers will be a perfect cube.

ANSWER:-

• The smallest number to be multiplied by 1681000 to make it a perfect cube is 41.
• The cube root of the number is 410.

GIVEN:-

• No. to be multiplied so that the product is a perfect cube = 1681000

TO FIND:-

• Smallest number whose product is a perfect cube = ?
• Cube root of the product = ?

SOLVING STEP BY STEP:-

• Factors of 1681000 is = 2×2×2×5×5×5×41×41
• Factors of 1681000 is = 2³×5³×41²
• We need 1 more 41 to make 1681000 a perfect cube.

So, we have to multiply 1681000 by 41 to get a perfect cube.

• To make 1681000 a perfect cube = 1681000×41
• To make 1681000 a perfect cube = 68921000
• Cube root of the product = ³√68921000
• Cube root of the product = ³√68921000 = 410
• Cube root of the product = 410

Hence, the cube root of the product is 410.

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