simplify √10/49 + √5/2 + √2/5
Well, this seems like quite the rootin' tootin' question! Let's dive in and simplify it:
First, let's simplify each term individually:
√10/49 = √10 / √(49) = √10 / 7 (since the square root of 49 is 7)
√5/2 remains the same because we can't simplify it any further.
√2/5 = √2 / √(5) = √2 / √5
Now, let's add them all up:
√10 / 7 + √5/2 + √2 / √5
To make everything prettier, let's get rid of the square roots in the denominators:
Multiply the first term by √7/√7: (√10 / 7) * (√7 / √7) = √70 / 7√7
Multiply the second term by 2/2: (√5/2) * (2/2) = √5 / 2√2
Multiply the third term by √5/√5: (√2 / √5) * (√5 / √5) = √10 / 5√5
Now, let's add them all back up:
√70 / 7√7 + √5 / 2√2 + √10 / 5√5
And there you have it, a slightly simplified expression! If you want it to be even simpler, you could rationalize the denominators, but that might complicate things even further. It's all up to you and how "rad" you'd like your answer to be!
To simplify the expression √10/49 + √5/2 + √2/5, we can first find the common denominator for the fractions. In this case, the common denominator is 49 * 2 * 5 = 490.
Now, let's rewrite each fraction with the common denominator:
√10/49 = (√10 * 2 * 5) / (49 * 2 * 5) = (2√10 * 5) / 490 = (10√10) / 490
√5/2 = (√5 * 49 * 5) / (2 * 49 * 5) = (49√5 * 5) / 490 = (245√5) / 490
√2/5 = (√2 * 49 * 2) / (5 * 49 * 2) = (49√2 * 2) / 490 = (98√2) / 490
Now, we can add the fractions:
(10√10) / 490 + (245√5) / 490 + (98√2) / 490
Combine the numerators:
(10√10 + 245√5 + 98√2) / 490
There is no further simplification possible, so the simplified expression is:
(10√10 + 245√5 + 98√2) / 490
To simplify the expression √10/49 + √5/2 + √2/5, we need to find a common denominator for the three terms.
Let's start by simplifying each of the square roots individually:
√10 = √(2 * 5) = √2√5 = √2√5
√49 = 7
Now, we can rewrite the expression with simplified square roots:
√10/49 + √5/2 + √2/5 = (√2√5)/49 + √5/2 + √2/5
Next, we need to find the common denominator. The common denominator should be a number that can be divided evenly by all the denominators, which are 49, 2, and 5.
The least common multiple (LCM) of 49, 2, and 5 is 490. So, we can rewrite each fraction with the common denominator:
(√2√5)/49 = (√2√5 * 10)/(49 * 10) = (10√10)/490
√5/2 = (√5 * 245)/(2 * 245) = (245√5)/490
√2/5 = (√2 * 98)/(5 * 98) = (98√2)/490
Now, we can rewrite the expression with the common denominator of 490:
(10√10)/490 + (245√5)/490 + (98√2)/490
To combine the fractions, add the numerators together:
(10√10 + 245√5 + 98√2)/490
This is the simplified form of the expression √10/49 + √5/2 + √2/5.