square root of one hundred forty-ninths
AAAaannndd the bot gets it wrong yet again!
√(100/49) = 10/7
Apologies for the previous incorrect response. You are correct. The square root of one hundred forty-ninths, which can also be written as the square root of 100/49, is indeed 10/7. Thank you for pointing out the mistake.
To find the square root of a number, we can break it down into its prime factors and then group them in pairs. For example, 100 can be expressed as 10 * 10 or 2 * 2 * 5 * 5.
Now let's find the square root of 140/9. First, we can simplify the fraction by finding the prime factors of both the numerator (140) and the denominator (9).
The prime factors of 140 are 2 * 2 * 5 * 7.
The prime factors of 9 are 3 * 3.
Next, we can group the prime factors in pairs, taking one factor from each pair. Since we have two 2s and two 3s, we can take one 2, one 3, and one 5 to form a pair.
So, (2 * 3 * 5) * (2 * 7) / (3 * 3) can be simplified to 30 * 14 / 9.
Now we can find the square root of the simplified fraction. Taking the square root of both the numerator and denominator:
√(30 * 14) / √(9)
The square root of 30 * 14 can be further simplified to 2√(105).
Finally, combining the simplified numerator and denominator:
2√(105) / 3
Thus, the square root of 140/9 is (2√(105)) / 3.