Question

find the smallest number by which 59400 must be multiplied to make the product a perfect cube. also find the cube root of the product.​

Answer 1

Given :

59400

To find :

1. Smallest Number by which given number must be multiplied to make the product a perfect cube.
2. Cube root of product (new Number)

Method used :

• First of all find prime factor of given number
• Then make group of prime factor such that each group contain Same number 3 time { example (2×2×2) }
• Then multiply the given number by Number whose pairs can't be formed { like 5 } , so to make a group of 3

Solution :

Part 1 :

Prime factor -

59400 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 11

59400 = (2×2×2) × (3×3×3) × (5×5) × (11)

So , we should multiply by , (5 × 11 × 11 )

New Number = 59400 × 605

New number = 35937000

Part 2 :

Cube root of new Number

35937000 = (2×2×2) × (3×3×3) × (5×5×5) × (11×11×11)

$\sf \implies \: \sqrt[ 3 ]{35937000} = \sqrt[3]{ (2 \times 2 \times 2) \times (3 \times 3 \times 3) \times (5 \times 5 \times 5) \times (11 \times 11 \times 11)} \\ \\ \sf \implies \: \sqrt[ 3 ]{35937000} = \sqrt[3]{ {2}^{3} \times {3}^{3} \times {5}^{3} \times {11}^{3} } \\ \\ \sf \implies \: \sqrt[ 3 ]{35937000} = \sqrt[3]{( {2 \times 3 \times 5 \times 11)}^{3} } \\ \\ \sf \implies \: \sqrt[ 3 ]{35937000} = \: 2 \times 3 \times 5 \times 11 \\ \\ \sf \implies \: \sqrt[ 3 ]{35937000} \: = \: 330$

ANSWER :

1. 605
2. 330

Answer 2

Answer:

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Step-by-step explanation:

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