What is the simplified form of the following expression?
sqrt18 + sqrt72 - sqrt2
list the expression then list it simplified.
The expression is:
√18 + √72 - √2
To simplify this expression, we can simplify the square roots of the numbers. We know that the square root of 18 can be simplified as the square root of 9 times the square root of 2, since 9 is a perfect square:
√18 = √(9 * 2) = √9 * √2 = 3√2
Similarly, the square root of 72 can be simplified as:
√72 = √(36 * 2) = √36 * √2 = 6√2
Now we can substitute these simplified expressions back into the original expression:
3√2 + 6√2 - √2
Now we can combine like terms by adding the square root terms:
(3√2 + 6√2) - √2 = 9√2 - √2 = 8√2
Therefore, the simplified form of the expression √18 + √72 - √2 is 8√2.