Question

difference of two numbers, which are perfect cubes, is 189. if the cube root of the smaller of the two numbers, is 3,find the cube root of the larger number​

Answer 1

Answer :-

The cube root of the larger number is 6.

Solution :-

Cube root of smaller number of the two numbers = 3

Let the cube root of the larger number be x

Given

Difference of two numbers which are perfect cubes = 189

⇒ (Cube root of larger number)³ - (Cube root of smaller number)³ = 189

⇒ (x)³ - (3)³ = 189

⇒ x³ - 27 = 189

⇒ x³ = 189 + 27

⇒ x³ = 216

⇒ x = ³√216

⇒ x = 6

Therefore the cube root of the larger number is 6.

Answer 2

AnswEr :

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$</u><u>\</u><u>r</u><u>e</u><u>d</u><u>{</u><u>\</u><u>h</u><u>u</u><u>ge \boxed{ \bold{ \sqrt[3]{216} = 6 }}</u><u>}</u><u>$

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Explanation :

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☑ Given :

• Difference of two Numbers which are Perfect Cubes is 189.

• Cube Root of Smaller Number is 3

━━━━━━━━━━━━━━━━━━━━━━━━

☑ To Find :

• Cube Root of Larger Number.

━━━━━━━━━━━━━━━━━━━━━━━━

☑ Solution :

» Let the Larger Number be x.

A.T.Q.

➟ (Larger No.)³ - (Smaller No.)³ = 189

➟ (x)³ - (3)³ = 189

➟ x³ - (3 × 3 × 3) = 189

➟ x³ - 27 = 189

➟ x³ = 189 + 27

➟ x³ = 216

➟ x = $\sqrt[3]{216}$

➟ x = $\sqrt[3]{6 \times 6 \times 6}$

➟ x = 6

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$\therefore$ Cube Root of Larger Number is 6.