Add ^3√22 + 3√22 +√22 .(1 point)
^3√22 + 3√22 +√22 can be simplified as:
(1 + 3 + 1)√22 = 5√22
So, the answer is 5√22.
To solve this expression, we need to simplify each term individually before adding them together.
Let's simplify each term:
1) ^3√22
To simplify a cube root, we need to find the number which, when multiplied by itself three times, is equal to 22.
To find this number, we can start by taking an educated guess. Let's try 2: 2 x 2 x 2 = 8, which is smaller than 22. Let's try a bigger number, say 3: 3 x 3 x 3 = 27, which is greater than 22.
By trying a few more numbers, we find that 22 is close to 2.8 cubed.
So, ^3√22 is approximately 2.8.
2) 3√22
To simplify a square root, we try to find the largest perfect square that divides evenly into the number.
22 is not a perfect square, but it can be written as the product of two parts: 2 x 11.
Now we can simplify the square root by taking the square root of the perfect square part (2) and leaving the non-perfect square part (11) under the radical sign.
So, 3√22 = 3√(2 x 11) = 3√2√11.
Note that square root and cube root are different operations, so we cannot simplify this term any further.
3) √22
Similar to the previous step, we try to find the largest perfect square that divides evenly into 22.
22 is not a perfect square, and it cannot be simplified any further.
So, √22 cannot be simplified.
Now, we can add all three terms together:
^3√22 + 3√22 + √22 = 2.8 + 3√(2 x 11) + √22.
There is no like term to combine with the cube root and the square root terms, so the simplest form of the expression is:
2.8 + 3√(2 x 11) + √22.
To simplify the expression ^3√22 + 3√22 + √22, we can combine like terms.
Since all terms have the same radicand (√22) but different indices (3, 1, and none), we can add the coefficients and keep the radicand the same.
^3√22 + 3√22 + √22 = (1 + 3 + 1)√22
Adding the coefficients gives:
= 5√22
Therefore, ^3√22 + 3√22 + √22 simplifies to 5√22.