Adding and subtracting radicals
3radical sign 5/12 + radical sign12/5 - 1/3radical sign 60 =
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To add and subtract radicals, you need to simplify the radicals and then combine like terms.
Let's simplify the radicals first:
For 3√5/12, start by simplifying the fraction 5/12:
The prime factors of 5 are 5, so it cannot be simplified.
The prime factors of 12 are 2, 2, and 3. There is one 2 common between the numerator and denominator that can be canceled out.
√5/12 = √5/2√3
For √12/5, start by simplifying the fraction 12/5:
The prime factors of 12 are 2, 2, and 3. There is one 2 common between the numerator and denominator that can be canceled out.
√12/5 = 2√3/5
For 1/(3√60), start by simplifying the radical √60:
The prime factors of 60 are 2, 2, 3, and 5. There is one 2 common between the numerator and denominator that can be canceled out.
√60 = 2√15
1/(3√60) = 1/(3 * 2√15)
Now let's substitute the simplified radicals back into the original expression:
3√5/2√3 + 2√3/5 - 1/(3 * 2√15)
To combine like terms, we need to have the same radical in the denominator. Let's multiply the first term by 5/5, and the second term by 2√3/ 2√3, it equals:
(15√5)/(10√3) + (4√3)/(10√3) - (1/(3 * 2√15))
Combining the numerators:
(15√5 + 4√3)/(10√3) - (1/(3 * 2√15))
Since we have the same denominator, we can combine the fractions:
(15√5 + 4√3 - 1)/(10√3)
So, the simplified expression is:
(15√5 + 4√3 - 1)/(10√3)