Add 2√8 + √28 + 2√8.
To simplify the expression 2√8 + √28 + 2√8, first simplify the radicands (numbers inside the square roots) if possible.
√8 = √(4 * 2) = 2√2
√28 = √(4 * 7) = 2√7
Now substitute these simplified values back into the expression:
2√8 + √28 + 2√8 = 2(2√2) + 2√7 + 2(2√2)
Now combine like terms:
4√2 + 2√7 + 4√2 = 8√2 + 2√7
the correct answer to the question is 4√8 + √28
Apologies for the mistake in the previous response. Let's correct it.
To simplify 2√8 + √28 + 2√8, first simplify the radicands:
√8 = √(4 * 2) = 2√2
√28 = √(4 * 7) = 2√7
Now substitute these simplified values back into the expression:
2√8 + √28 + 2√8 = 2(2√2) + √(4 * 7) + 2(2√2) = 4√2 + 2√7 + 4√2
Combining like terms:
4√2 + 2√7 + 4√2 = 8√2 + 2√7
Therefore, the simplified form of 2√8 + √28 + 2√8 is 8√2 + 2√7.
To solve this expression, we need to simplify each square root term and then combine like terms.
Let's start by simplifying the square root expressions.
√8 can be further simplified as √(4 * 2). Since 4 is a perfect square, we can take the square root of 4, which is 2, out of the square root, resulting in 2√2. So the first term, 2√8, can be simplified to 2√2.
Similarly, √28 can be simplified as √(4 * 7). Taking the square root of 4, which is 2, out of the square root gives us 2√7.
Now let's rewrite the expression after simplifying the square roots:
2√2 + 2√7 + 2√8
We have two terms with √2 in them, so we can combine them by adding their coefficients, which gives us 4√2.
Now our expression becomes:
4√2 + 2√7 + 2√8
We have simplified the expression by combining like terms and simplifying the square root terms.