1. Simplify the radical
Sqr of 3c² over the sqr of 27
√ ̅3c²
---------
√ ̅27
2. Simplify the radical
√27 ∙ √3
3. Simplify the radical
√ ̅75 - 4√ ̅75
4. Simplify the radical
(√3 + √2)²
1. c/3
2. 9
3. -15√3
4. 5+2√6
hey 1234 use the site symbolab it well show you the steps for each question.
1. sqrt(3c^2)/sqrt(27) = c*sqrt(3)/sqrt(9*3) = c* sqrt(3)/3*sqrt(3) = c/3.
2. sqrt(27)*sqrt(3) = sqrt(9*3)*sqrt(3) = 3*sqrt(3) * sqrt(3) = 3 * 3 = 9.
3. sqrt(75) - 4*sqrt(75) = -3*sqrt(75) = -3*sqrt(25*3) = -3*5*sqrt(3) = -15 * sqrt(3).
The student should do #4.
Thanks Henry makes sense now
4. (sqrt3+sqrt2)^2 - 3 + 2*sqrt(3*2) + 2 = 5 + 2*sqrt(6).
You are welcome.
I wrote those out and spent a few minutes looking at each
1. To simplify the radical √(3c²) / √(27), we can break down each square root separately and simplify.
First, let's simplify the numerator √(3c²). Since we have a square root of the square (c²), we can simplify it to c. Therefore, √(3c²) simplifies to c√3.
Next, let's simplify the denominator √(27). We can break down 27 into its prime factors: 27 = 3 * 3 * 3. Taking the square root, we have √27 = √(3 * 3 * 3) = √(3² * 3) = 3√3.
Now, we have c√3 / 3√3. Since both the numerator and denominator have a common factor of √3, we can cancel it out: c√3 / 3√3 = c / 3.
Therefore, the simplified radical of √(3c²) / √(27) is c / 3.
2. To simplify the radical √27 * √3, we can multiply the terms inside the square root together.
√27 = √(9 * 3) = √9 * √3 = 3√3.
Therefore, √27 * √3 simplifies to 3√3.
3. To simplify the radical √75 - 4√75, we can combine like terms.
Since both terms have the same root (√75), we can combine them by subtracting their coefficients. The coefficients of √75 are 1 and -4, respectively.
Therefore, √75 - 4√75 simplifies to (-3)√75.
4. To simplify the radical (√3 + √2)², we can expand the expression using the distributive property.
(√3 + √2)² = (√3 + √2)(√3 + √2)
Using the FOIL method to multiply the binomials, we get:
(√3 + √2)(√3 + √2) = (√3)(√3) + (√3)(√2) + (√2)(√3) + (√2)(√2)
Simplifying each term, we have:
(√3)(√3) = 3
(√3)(√2) = √6
(√2)(√3) = √6
(√2)(√2) = 2
Therefore, the simplified radical of (√3 + √2)² is 3 + 2√6 + 2√6 + 2, which can be further simplified to 5 + 4√6.