Express in simplest radical form. 3, square root of, 175, end square root, plus, 8, square root of, 112, end square root 3 175
To simplify this expression, we first need to find the prime factors of 175 and 112.
Prime factors of 175: 5, 5, 7
Prime factors of 112: 2, 2, 2, 2, 7
Now, we can simplify the expression:
√175 + 8√112
√(5^2 ⋅ 7) + 8√(2^4 ⋅ 7)
5√7 + 8(2^2 √7)
5√7 + 8(2 √7)
5√7 + 16√7
So, the expression simplified to simplest radical form is 21√7.
It was 21/7
I apologize for the misunderstanding. If the expression is 21/7, then it simplifies to 3.
Express in simplest radical form. square root of, 5, end square root, minus, 6, square root of, 5, end square root 5 −6 5
To simplify the expression, we can combine like terms:
√5 - 6√5
= (1 - 6)√5
= -5√5
So, the expression simplifies to -5√5.
Express in simplest radical form. minus, square root of, 6, end square root, plus, 4, square root of, 6, end square root − 6 +4 6
To simplify the expression, we can combine like terms:
-√6 + 4√6
= (-1 + 4)√6
= 3√6
So, the expression simplifies to 3√6.
Express in simplest radical form. minus, 6, square root of, 80, end square root, minus, square root of, 5, end square root −6 80 − 5
To simplify the expression, we can simplify the square roots separately:
√80 = √(16 * 5) = √16 * √5 = 4√5
√5 remains as it is.
Now, we can substitute the simplified square roots back into the expression:
-6√80 - √5 = -6(4√5) - √5 = -24√5 - √5
Combine like terms:
-25√5
So, the expression simplifies to -25√5.
Express in simplest radical form. 10, square root of, 7, end square root, minus, square root of, 7, end square root 10 7 − 7
To simplify this expression, we can treat the square root of 7 as a common factor:
10√7 - √7
Combine like terms:
(10 - 1)√7
Simplify further:
9√7
So, the expression simplifies to 9√7.
Express in simplest radical form. square root of, 5, end square root, square root of, 50, end square root 5 50
To simplify this expression, we can simplify each square root separately:
√5 remains as it is.
For √50, we can find the prime factors of 50: 2, 5, 5.
Therefore, √50 = √(2^1 * 5^2) = 5√2.
Now, we can substitute the simplified square roots back into the expression:
√5 * √50 = √5 * 5√2 = 5√5√2
Combine the square roots:
5√(5*2) = 5√10
So, the expression simplifies to 5√10.
Express in simplest radical form. start fraction, square root of, 150, end square root, divided by, square root of, 2, end square root, end fraction 2 150
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √2 is also √2.
√150/√2 = (√150 * √2) / (√2 * √2)
Simplify each term:
= √(150 * 2) / 2
= √300 / 2
= √(100 * 3) / 2
= (√100 * √3) / 2
= (10 * √3) / 2
= 5√3
So, the expression simplifies to 5√3.
Express in simplest radical form. start fraction, square root of, 12, end square root, divided by, square root of, 2, end square root, end fraction 2 12
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √2 is also √2.
√12/√2 = (√12 * √2) / (√2 * √2)
Simplify each term:
= √(12 * 2) / 2
= √24 / 2
We can simplify √24 by factoring out the largest perfect square:
= √(4 * 6) / 2
= (√4 * √6) / 2
= (2 * √6) / 2
= √6
So, the expression simplifies to √6.
Express in simplest radical form. start fraction, square root of, 720, end square root, divided by, square root of, 9, end square root, end fraction 9 720
To simplify this expression, we first need to simplify the square roots separately:
√720 = √(144 * 5) = √144 * √5 = 12√5
√9 = 3
Now we can substitute the simplified square roots back into the expression:
√720 / √9 = (12√5) / 3
Simplify the fraction:
12√5 / 3 = (12/3)√5 = 4√5
So, the expression simplifies to 4√5.