How do you do radical expressions?
Square root of 72.
Cube root of 54.
Fourth root of 96.
To simplify radical expressions, you need to understand how to find the square root, cube root, or any other root of a number. Here's how you can solve the given examples step by step:
1. Square root of 72:
To find the square root of 72, you can factorize 72 and look for pairs of identical numbers. The square root of a pair of identical numbers will simplify to just that number. Let's break it down:
72 = 2 x 2 x 2 x 3 x 3
Now, group the numbers in pairs:
72 = (2 x 2) x (2 x 3) x (3 x 3)
= 2 x 2 x 3 x 3
= 2^2 x 3^2
The square root of (2^2 x 3^2) is simply 2 x 3 = 6.
Therefore, the square root of 72 is 6.
2. Cube root of 54:
Similar to the square root, you can also find the cube root by looking for factors in groups of three. Let's find the cube root of 54:
54 = 2 x 3 x 3 x 3
Grouping the numbers:
54 = 2 x (3 x 3) x 3
= 2 x 3^2
The cube root of (2 x 3^2) is 2 x 3 = 6.
Thus, the cube root of 54 is 6.
3. Fourth root of 96:
To find the fourth root, you'll need to look for factors in groups of four. Let's determine the fourth root of 96:
96 = 2 x 2 x 2 x 2 x 3
Grouping the numbers:
96 = (2 x 2) x (2 x 2) x 3
= 2^2 x 2^2 x 3
The fourth root of (2^2 x 2^2 x 3) is just 2 x 2 x 3 = 12.
Hence, the fourth root of 96 is 12.
Remember, these steps involve factoring the number and grouping factors. The process remains the same for any other radical expressions.