Question

question 4
which value is equivalent to the value of $sqrt3{729}$?
$sqrt3{729} = 81$ because $729 \div 3 = 243$ and $243 \div 3 = 81$
$sqrt3{729} = 243$ because $729 \div 3 = 243$
$sqrt3{729} = 3$ because $(3^3)^2 = 729$
$sqrt3{729} = 9$ because $9 \cdot 9 \cdot 9 = 729$
question 5

Explanation:

Step1: Recall the definition of cube root

The cube root of a number \( x \), denoted as \( \sqrt[3]{x} \), is a number \( y \) such that \( y^3 = x \). So we need to find a number \( y \) where \( y\times y\times y=729 \).

Step2: Test each option

• For the first option: \( 81\times81\times81 \) is way larger than 729, so \( \sqrt[3]{729}

eq81 \).

• For the second option: \( 243\times243\times243 \) is much larger than 729, so \( \sqrt[3]{729}

eq243 \).

• For the third option: \( 3^3 = 27 \), \( (3^3)^2=3^6 = 729 \), but we need \( y^3=729 \), not \( y^2 \) related to \( 3^3 \). So this is incorrect.
• For the fourth option: \( 9\times9\times9=729 \), so by the definition of cube root, \( \sqrt[3]{729} = 9 \) because \( 9^3=729 \).

Answer:

The option \(\sqrt[3]{729} = 9\) because \( 9\cdot9\cdot9 = 729 \) (the fourth option among the given choices for Question 4)