add ^3√ 22 + 3√ 22+ √ 22
a. 5√66
b 3^√ 22+ 4√ 44
c. 5√22
d. 3√ 22+ 4√ 22
To begin, let's simplify each term first:
^3√22 = (√22)^(3/2) = (22^(1/2))^(3/2) = 22^(3/4)
3√22 = 3(√22) = 3(22^(1/2))
√22 = 22^(1/2)
Now, let's substitute these simplified terms back into the expression:
^3√22 + 3√22 + √22 = 22^(3/4) + 3(22^(1/2)) + 22^(1/2)
Now, we can combine like terms:
22^(3/4) + 3(22^(1/2)) + 22^(1/2) = 22^(3/4) + 4(22^(1/2))
Therefore, the answer is d. 3√22 + 4√22
To simplify the given expression, let's work step-by-step.
Step 1: Simplify each individual radical term.
- ^3√22 cannot be simplified further because there are no perfect cubes that divide into 22.
- √22 cannot be simplified further because there are no perfect squares that divide into 22.
Step 2: Combine like terms.
- We have two terms with ^3√22 and one term with √22.
Step 3: Add the coefficients of the like terms.
- The coefficients of the ^3√22 terms are both 1.
- The coefficient of the √22 term is 1.
Step 4: Add the radical terms.
- ^3√22 + ^3√22 = 2 ^3√22
Final Answer: The simplified expression ^3√22 + 3√22 + √22 can be written as 2 ^3√22, so the correct option is d) 3√22 + 4√22.
To simplify the given expression ^3√ 22 + 3√ 22+ √ 22, we first need to evaluate each of the cube roots (∛), square roots (√), and constant terms separately. Here's how we can do it:
1. Simplify ^3√ 22:
To find the cube root of 22 (^3√ 22), we can use the property of exponents which states that ^(1/n)X = X^(1/n), where X is a positive number and n is a positive integer. Applying this property to the given expression, ^3√ 22 can be written as 22^(1/3).
2. Simplify 3√ 22:
To simplify 3√ 22, we can use the same property of exponents. 3√ 22 can be written as 22^(1/3) * 3.
3. Simplify √ 22:
To simplify √ 22, we can directly find the square root of 22. The square root of 22 (√ 22) is an irrational number, so it cannot be simplified further.
Now, let's combine the simplified terms:
22^(1/3) + 22^(1/3) * 3 + √ 22
Since both the first and second terms involve the cube root of 22, we can combine them:
2 * 22^(1/3) + √ 22
Thus, the simplified expression is 2 * 22^(1/3) + √ 22.
Unfortunately, none of the answer options provided match the simplified expression.