Question

find the cube root of 729 ​

Answer 1

Let's find the cube root of 729 step-by-step

∛729

Step 1: Prime factorize 729.

$\Large{ \begin{array}{c|c} \tt 3 & \sf{ 729} \\ \cline{1-2} \tt 3 & \sf { 243} \\ \cline{1-2} \tt 3 & \sf{ 81} \\ \cline{1-2} \tt 3 & \sf{27} \\ \cline{1-2} \tt 3 & \sf{ 9 }\\ \cline{1-2} \tt 3 & \sf{ 3 }\\ \cline{1-2} \tt & \sf{ 1} \\ \end{array}}$

729 ⇒ 3 × 3 × 3 × 3 × 3 × 3

Step 2: Group the factors obtained in brackets with the 3 same numbers in each.

729 ⇒ 3 × 3 × 3 × 3 × 3 × 3

729 ⇒ (3 × 3 × 3) × (3 × 3 × 3)

Step 3: To find the cube root, take one number from each bracket and then multiply them.

⇒ ∛729 = 3 × 3

⇒ ∛729 = 9

Step 4: Verify if the obtained cube root is correct by finding the cube of the cube root.

⇒ (9)³

⇒ 9 × 9 × 9

⇒ 729

∴ The cube root of 729 is 9

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Answer 2

Answer:

$\huge{\bf{\underline{\red{Answer :}}}}$

$\sqrt[3]{729} = \sqrt[3]{3 \times 3 ji \times 3 \times 3 \times 3 \times 3}$

$\Rightarrow$3 × 3

$\sqrt[3]{729}$ = 9