What is the square root for 3√729.
The Correct Answer and Explanation is :
Let’s start by solving ( 3\sqrt{729} ) and then find the square root of that result.
- Step 1: Calculate the cube root of 729. The cube root of a number ( a ) is the value ( b ) such that ( b^3 = a ). [
3\sqrt{729} = 9
] This is because ( 9^3 = 729 ). - Step 2: Calculate the square root of the result (9). The square root of a number ( c ) is the value ( d ) such that ( d^2 = c ). [
\sqrt{9} = 3
]
So, the answer to the expression ( \sqrt{3\sqrt{729}} ) is 3.
Explanation
Let’s break down the steps in more detail.
When working with radicals (roots), it’s useful to understand what each symbol means. The cube root (symbolized as ( 3\sqrt{} )) finds the number which, when multiplied by itself three times, gives the original number. In this case, ( 3\sqrt{729} ) means finding the cube root of 729, which is 9. We know this because ( 9 \times 9 \times 9 = 729 ).
Once we find the cube root, we then apply the square root operation to that result. The square root operation is finding the number which, when multiplied by itself, equals the original number. So, after finding ( 3\sqrt{729} = 9 ), we then find ( \sqrt{9} ), which equals 3.
Thus, each root operation reduces the value closer to the “core” number.