how to convert a root in the easiest way possible
Answers
Step-by-step explanation:
To simplify a square root: make the number inside the square root as small as possible (but still a whole number):
Example: √12 is simpler as 2√3
Get your calculator and check if you want: they are both the same value!
Here is the rule: when a and b are not negative
√(ab) = √a × √b
And here is how to use it:
Example: simplify √12
12 is 4 times 3:
√12 = √(4 × 3)
Use the rule:
√(4 × 3) = √4 × √3
And the square root of 4 is 2:
√4 × √3 = 2√3
So √12 is simpler as 2√3
Another example:
Example: simplify √8
√8 = √(4×2) = √4 × √2 = 2√2
(Because the square root of 4 is 2)
And another:
Example: simplify √18
√18 = √(9 × 2) = √9 × √2 = 3√2
It often helps to factor the numbers (into prime numbers is best):
Example: simplify √6 × √15
First we can combine the two numbers:
√6 × √15 = √(6 × 15)
Then we factor them:
√(6 × 15) = √(2 × 3 × 3 × 5)
Then we see two 3s, and decide to "pull them out":
√(2 × 3 × 3 × 5) = √(3 × 3) × √(2 × 5) = 3√10
Fractions
There is a similar rule for fractions:
root a / root b = root (a / b)